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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Differentiation in reproductive potential and chemical communication of reproductive status in workers and queens of the ant Myrmecia gulosa

Dietemann, Vincent. January 2002 (has links)
Würzburg, University, Diss., 2002. / Dateien im PDF-Format.
2

Biological control of Marmara gulosa Guillén and Davis in the San Joaquin Valley : a thesis /

Kirkland, Crystal Allina. Costello, Michael J. January 1900 (has links)
Thesis (M.S.)--California Polytechnic State University, 2009. / Mode of access: Internet. Title from PDF title page, viewed on March 30, 2009. Major professor: David Headrick. "Presented to the Electrical Engineering Department Faculty of California Polytechnic State University, San Luis Obispo." "In partial fulfillment of the requirements for the degree of Master of Science in Agriculture, with specialization in Crop Science." "February 2009." Includes bibliographical references (p. 181-187). Will also be available on microfiche.
3

Differentiation in reproductive potential and chemical communication of reproductive status in workers and queens of the ant Myrmecia gulosa / Differenzierung des reproduktiven Potentials und chemische Kommunikation des reproduktiven Status von Arbeiterinnen und Königinnen der Ameise Myrmecia gulosa

Dietemann, Vincent January 2002 (has links) (PDF)
Division of reproductive labour in societies represents a topic of interest in evolutionary biology at least since Darwin. The puzzle of how helpers can be selected for, in spite of their reduced fertility has found an explanation in the kin selection theory: workers can overcome the cost of helping and of forgiving direct reproduction by rearing sufficiently related individuals. However, in the Hymenoptera, little is known on the proximate mechanisms that regulate the division of labour in colonies. Our knowledge is based on several "primitive" ants from the subfamily Ponerinae and two highly eusocial Hymenoptera species. In the former, the dominance hierarchies allowing for the establishment of individuals as reproductives are well understood. In contrast, the pheromonal mechanisms that help maintain their reproductive status are not understood. Similarly in "higher" ants, pheromonal regulation mechanisms of worker reproduction by queens remain largely unknown. The aim of this study is to determine the modalities of production, distribution and action, as well as the identity of the queen pheromones affecting worker reproduction in the ant Myrmecia gulosa. This species belongs to the poorly studied subfamily Myrmeciinae, which is endemic to the Australian region. The subfamily represents, together with the Ponerinae, the most "primitive" ants: their morphology is close to that of the hypothetical ancestor of ants, and the specialisation of queens is weaker than that of "higher" ants. Simple regulation mechanisms were therefore expected to facilitate the investigation. The first step in this study was to characterise the morphological specialisation of queens and workers, and to determine the differences in reproductive potential associated with this specialisation. This study contributes to our understanding of the link between regulation of division of reproductive labour and social complexity. Furthermore, it will help shed light on the reproductive biology in the poorly known subfamily Myrmeciinae. Queens were recognised by workers on the basis of cuticular as well as gland extracts or products. What is the exact function of the multiple pheromones identified and how they interact remains to be determined. This could help understand why queen "signal" in a "primitive" ant with weakly specialised queens such as M. gulosa appears to be as complex as in highly eusocial species. Primer pheromones act on workers? physiology and have long-term effect. Whether workers of M. gulosa reproduce or not is determined by the detection of a queen pheromone of this type. Direct physical contact with the queen is necessary for workers to detect this pheromone. Thus, the colony size of M. gulosa is compatible with a simple system of pheromone perception by workers based on direct physical contact with the queen. When prevented from establishing physical contact with their queen, some workers start to reproduce and are policed by nestmates. The low volatility of the cuticular hydrocarbons (CHCs), their repartition over the entire cuticle and the existence of queen and worker specific CHC profiles suggest that these chemicals constitute a queen pheromone. Importance of HC versus non-HC compounds was confirmed by bioassaying purified fraction of both classes of chemicals. This study demonstrates for the first time that purified HCs indeed are at the basis of the recognition of reproductive status. This supports the idea that they are also at the basis of the recognition of queens by their workers. As CHCs profiles of workers and queens become similar with acquisition of reproductive status, they represent honest fertility markers. These markers could be used as signals of the presence of reproductives in the colonies, and represent the basis of the regulation of division of reproductive labour. / In der Evolutionsbiologie stellt die Arbeitsteilung in Sozietäten spätestens seit Darwin ein Interessensgebiet dar. Die Frage nach der Selektion von Helfern, trotz ihrer reduzierten Fruchtbarkeit, hat eine Erklärung in der Verwandenselektionstheorie gefunden: Arbeiterinnen können die Kosten des Helfens und eingeschränkter direkter Fortpflanzung überwinden, indem sie ausreichend verwandte Individuen aufziehen. Bei den Hymenopteren ist über die proximaten Mechanismen, welche die Arbeitsteilung in den Kolonien regulieren, allerdings nur wenig bekannt. Unser Wissen basiert auf den Ergebnissen von wenigen Untersuchungen an einigen "primitiven" Ameisen der Unterfamilie Ponerinae und zwei hochsozialen Hymenoptera-Arten. Bei "primitiven" Ameisenarten sind die Dominanzhierachien welche die Bildung von fortpflanzungsfähigen Individuen erlauben, gut untersucht. Im Gegensatz dazu sind die chemischen Signale, welche ihren reproduktiven Status aufrechterhalten, noch nicht aufgeklärt. Ebenso sind die pheromonellen Regulationsmechanismen der Arbeiterinnenreproduktion durch die Königin in "höherentwickelten" Ameisenarten weitgehend unbekannt. Das Ziel der Studie an Myrmecia gulosa war die Bestimmung der Modalitäten von Produktion, Verbreitung und Funktion der Königinpheromone, sowie Aufklärung ihrer stofflichen Zusammensetzung. Die untersuchte Art gehört zu den bisher wenig beachteten Myrmeciinae und kommt endemisch in Australien vor. Zusammen mit den Ponerinae weist diese Subfamilie die "primitivsten" Ameisenarten auf. Die Morphologie der Ameisen ist angelehnt an die der hypothetischen Vorfahren und ihre soziale Organisation ist weniger komplex als die "höherentwickelter" Arten. Es wurden daher einfache Mechanismen erwartet, die helfen sollten, die Regulation der reproduktiven Arbeitsteilung bei "primitiven" Ameisen mit einer morphologisch spezialisierten Königin zu verstehen. Der erste Teil der Studie sollte die morphologische Spezialisation der Königinnen und der Arbeiterinnen charakterisieren, bzw. den Unterschied im reproduktiven Potential, welcher mit dieser Spezialisierung verbunden ist, bestimmen. Die Untersuchung trägt zum Verständnis der Verknüpfungen zwischen Regulation der reproduktiven Arbeitsteilung und sozialer Komplexität bei. Überdies wird sie helfen, Licht auf die Fortpflanzungsbiologie der wenig bekannten Subfamilie der Myrmeciinae zu werfen. Königinen werden von den Arbeiterinnen aufgrund ihrer kutikulären sowie ihrer exokrinen Extrakte oder Produkte erkannt. Die exakte Funktion der multiplen Pheromone und wie sie interagieren muß noch untersucht werden. Allerdings könnte dies helfen zu verstehen, warum "Königinsignale" bei einer "primitiven" Ameise wie M. gulosa, mit einer wenig spezialisierten Königin, anscheinend komplexer sind, als in höheren eusozialen Arten. Primer-Pheromone wirken sich auf die Physiologie der Arbeiterinnen aus und haben einen Langzeiteffekt. Ob Arbeiterinnen von M. gulosa reproduzieren oder nicht, hängt von der Erkennung eines Königinpheromons dieser Art ab. Nur nach direktem physischen Kontakt mit ihrer Königin nehmen die Arbeiterinnen dieses Pheromon wahr. Daher paßt die Koloniegröße von M. gulosa zu dem einfachen System der Pheromonwahrnehmung basierend auf direktem physischen Kontakt zur Königin. Wenn physischer Kontakt zur Königin unterbunden wird, beginnen einige Arbeiterinnen mit der Reproduktion werden dann aber von Nestgenossen durch "Policing" davon abgehalten. Die geringe Flüchtigkeit von der Kutikuläre Kohlenwasserstoffe (KKW´s), ihre Verteilung über den ganzen Körper und die Existenz von königin- und arbeiterspezifischen KKW-Profilen deuten auf ihre Funktion als Königinpheromon hin. Um die Bedeutung der Komponenten zu unterstreichen, wurden KW-Fraktionen gegen Nicht-KW-Fraktionen in Biotests untersucht. Diese Studie demonstriert zum ersten Mal, dass die KW Fraktion tatsächlich die Basis zur Erkennung des reproduktiven Status bilden. Das unterstützt auch die Idee, dass sie als Grundlage für die Erkennung der Königin durch die Arbeiterinnen dienen. Die Kohlenwasserstoffprofile von Arbeiterinnen und Königin gleichen sich mit Erwerb des reproduktiven Status aneinander an. Sie könnten somit ein ehrliches Erkennungsmerkmal für Fruchtbarkeit darstellen. Diese Merkmale könnten als ehrliches Signal der Anwesenheit reproduktiver Individuen in der Kolonie benutzt werden und die Basis der Regulation der reproduktiven Arbeitsteilung darstellen.
4

Estudo de casos de complexidade de colorações gulosa de vértices e de arestas / Case studies of complexity of greedy colorings of vertices and edges

Oliveira, Ana Karolinna Maia de January 2011 (has links)
OLIVEIRA, Ana Karolinna Maia de. Estudo de casos de complexidade de colorações gulosa de vértices e de arestas. 2011. 58 f. Dissertação (Mestrado em ciência da computação)- Universidade Federal do Ceará, Fortaleza-CE, 2011. / Submitted by Elineudson Ribeiro (elineudsonr@gmail.com) on 2016-07-08T18:03:48Z No. of bitstreams: 1 2011_dis_akmoliveira.pdf: 520341 bytes, checksum: b0c0d48f19d7c3e376c2c79c3a815b08 (MD5) / Approved for entry into archive by Rocilda Sales (rocilda@ufc.br) on 2016-07-13T12:34:49Z (GMT) No. of bitstreams: 1 2011_dis_akmoliveira.pdf: 520341 bytes, checksum: b0c0d48f19d7c3e376c2c79c3a815b08 (MD5) / Made available in DSpace on 2016-07-13T12:34:49Z (GMT). No. of bitstreams: 1 2011_dis_akmoliveira.pdf: 520341 bytes, checksum: b0c0d48f19d7c3e376c2c79c3a815b08 (MD5) Previous issue date: 2011 / The vertices and edges colorings problems, which consists in determine the smallest number of colors needed to color the vertices and edges of a graph, respectively, so that adjacent vertices and adjacent edges, respectively, have distinct colors, are computationally hard problems and recurring subject of research in graph theory due to numerous practical problems they model. In this work, we study the worst performance of greedy algorithms for coloring vertices and edges. The greedy algorithm has the following general principle: to receive, one by one, the vertices (respect. edges) of the graph to be colored by assigning always the smallest possible color to the vertex (resp. edge) to be colored. We note that so greedy coloring the edges of a graph is equivalent to greedily coloring its line graph, this being the greatest interest in research on greedy edges coloring. The worst performance of the Algorithms is measured by the greatest number of colors they can use. In the case of greedy vertex coloring, this is the number of Grundy or greedy chromatic number of the graph. For the edge coloring, this is the greedy chromatic index or Grundy index of the graph. It is known that determining the Grundy number of any graph is NP-hard. The complexity of determining the Grundy index of any graph was however an open problem. In this dissertation, we prove two complexity results. We prove that the Grundy number of a (q,q−4)-graph can be determined in polynomial time. This class contains strictly the class of cografos P4-sparse for which the same result had been established. This result generalizes so those results. The presented algorithm uses the primeval decomposition of graphs, determining the parameter in linear time. About greedy edge coloring, we prove that the problem of determining the Grundy index is NP-complete for general graphs and polynomial for catepillar graphs, implying that the Grundy number is polynomial for graphs of line of caterpillars. More specifically, we prove that the Grundy index of a caterpillar is D or D+1 and present a polynomial algorithm to determine it exactly. / Os problemas de coloracão de vértices e de arestas, que consistem em determinar o menor número de cores necessárias para colorir os vértices e arestas de um grafo, respectivamente, de forma que vértices adjacentes e arestas adjacentes, respectivamente, possuem cores distintas, são problemas computacionalmente difíceis e são objeto de pesquisa recorrente em teoria do grafos em virtude de inúmeros problemas práticos que eles modelam. No presente trabalho, estudamos o pior desempenho dos algoritmos gulosos de coloração de vértices e de arestas. O algoritmo guloso tem o seguinte princípio geral: receber, um a um, os vértices (respect. as arestas) do grafo a ser colorido, atribuindo sempre a menor cor possível ao vértice (resp. aresta) a ser colorido. Observamos que colorir de forma gulosa as arestas de um grafo equivale a colorir de forma gulosa o seu grafo linha, tendo sido este o maior interesse na pesquisa em coloração gulosa de arestas. O pior desempenho dos algoritmos é medido pelo maior número de cores que eles podem utilizar. No caso da coloração gulosa de vértices, esse é o número de Grundy ou número cromático guloso do grafo. No caso da coloração de arestas, esse é o íındice cromático guloso ou íındice de Grundy do grafo. Sabe-se que determinar o número de Grundy de um grafo qualquer é NP-difícil. A complexidade de determinar o índice de Grundy de um grafo qualquer era entretanto um problema em aberto. Na presente dissertação, provamos dois resultados de complexidade. Provamos que o número de Grundy de um grafo (q,q−4) pode ser determinado em tempo polinomial. Essa classe contém estritamente a classe dos cografos e P4-esparsos para os quais o mesmo resultado havia sido estabelecido. Esse resultado generaliza portanto aqueles resultados. O algoritmo apresentado usa a decomposição primeval desses grafos, determinando o parâmetro em tempo linear. No que se refere à coloração de arestas, provamos que o problema de determinar o índice de Grundy é NP-completo para grafos em geral e polinomial para grafos caterpillar, implicando que o número de Grundy é polinomial para os grafos linha desses. Mais especificamente provamos que o índice de Grundy dos caterpillar é D ou D+1 e apresentamos um algoritmo polinomial para determiná-lo exatamente.
5

Estudo de casos de complexidade de coloraÃÃes gulosa de vÃrtices e de arestas / Case studies of complexity of greedy colorings of vertices and edges

Ana Karolinna Maia de Oliveira 07 April 2011 (has links)
Os problemas de colorac Ëao de vÂertices e de arestas, que consistem em determinar o menor nÂumero de cores necessÂarias para colorir os vÂertices e arestas de um grafo, respectivamente, de forma que vÂertices adjacentes e arestas adjacentes, respectivamente, possuem cores distintas, sËao problemas computacionalmente difÂıceis e sËao objeto de pesquisa recorrente em teoria do grafos em virtude de inÂumeros problemas prÂaticos que eles modelam. No presente trabalho, estudamos o pior desempenho dos algoritmos gulosos de colorac Ëao de vÂertices e de arestas. O algoritmo guloso tem o seguinte princÂıpio geral: receber, um a um, os vÂertices (respect. as arestas) do grafo a ser colorido, atribuindo sempre a menor cor possÂıvel ao vÂertice (resp. aresta) a ser colorido. Observamos que colorir de forma gulosa as arestas de um grafo equivale a colorir de forma gulosa o seu grafo linha, tendo sido este o maior interesse na pesquisa em colorac Ëao gulosa de arestas. O pior desempenho dos algoritmos Âe medido pelo maior nÂumero de cores que eles podem utilizar. No caso da colorac Ëao gulosa de vÂertices, esse Âe o nÂumero de Grundy ou nÂumero cromÂatico guloso do grafo. No caso da colorac Ëao de arestas, esse Âe o Âındice cromÂatico guloso ou Âındice de Grundy do grafo. Sabe-se que determinar o nÂumero de Grundy de um grafo qualquer Âe NP-difÂıcil. A complexidade de determinar o Âındice de Grundy de um grafo qualquer era entretanto um problema em aberto. Na presente dissertac Ëao, provamos dois resultados de complexidade. Provamos que o nÂumero de Grundy de um grafo (q,q−4) pode ser determinado em tempo polinomial. Essa classe contÂem estritamente a classe dos cografos e P4-esparsos para os quais o mesmo resultado havia sido estabelecido. Esse resultado generaliza portanto aqueles resultados. O algoritmo apresentado usa a decomposicÂËao primeval desses grafos, determinando o parËametro em tempo linear. No que se refere `a colorac Ëao de arestas, provamos que o problema de determinar o Âındice de Grundy Âe NP-completo para grafos em geral e polinomial para grafos caterpillar, implicando que o nÂumero de Grundy Âe polinomial para os grafos linha desses. Mais especificamente provamos que o Âındice de Grundy dos caterpillar Âe D ou D+1 e apresentamos um algoritmo polinomial para determinÂa-lo exatamente. / The vertices and edges colorings problems, which consists in determine the smallest number of colors needed to color the vertices and edges of a graph, respectively, so that adjacent vertices and adjacent edges, respectively, have distinct colors, are computationally hard problems and recurring subject of research in graph theory due to numerous practical problems they model. In this work, we study the worst performance of greedy algorithms for coloring vertices and edges. The greedy algorithm has the following general principle: to receive, one by one, the vertices (respect. edges) of the graph to be colored by assigning always the smallest possible color to the vertex (resp. edge) to be colored. We note that so greedy coloring the edges of a graph is equivalent to greedily coloring its line graph, this being the greatest interest in research on greedy edges coloring. The worst performance of the Algorithms is measured by the greatest number of colors they can use. In the case of greedy vertex coloring, this is the number of Grundy or greedy chromatic number of the graph. For the edge coloring, this is the greedy chromatic index or Grundy index of the graph. It is known that determining the Grundy number of any graph is NP-hard. The complexity of determining the Grundy index of any graph was however an open problem. In this dissertation, we prove two complexity results. We prove that the Grundy number of a (q,q−4)-graph can be determined in polynomial time. This class contains strictly the class of cografos P4-sparse for which the same result had been established. This result generalizes so those results. The presented algorithm uses the primeval decomposition of graphs, determining the parameter in linear time. About greedy edge coloring, we prove that the problem of determining the Grundy index is NP-complete for general graphs and polynomial for catepillar graphs, implying that the Grundy number is polynomial for graphs of line of caterpillars. More specifically, we prove that the Grundy index of a caterpillar is D or D+1 and present a polynomial algorithm to determine it exactly.
6

Biological Control of Marmara gulosa Guillén and Davis in the San Joaquin Valley

Kirkland, Crystal A 01 February 2009 (has links) (PDF)
Peelminer, Marmara gulosa Davis and Guillén, has been reported as a sporadic pest in California and Arizona since 1998. Marmara gulosa has been a persistent pest in the San Joaquin Valley of California (USA) since 1998. Prior to 2000 the only reports of high populations of citrus peelminer were in the Coachella Valley. The larval stages of M. gulosa create serpentine mines scarring the upper epidermal layers of citrus rind, rendering it unacceptable for fresh market sale. Chemicals have failed to provide adequate control of M. gulosa; thus, the use of natural enemies is considered the best long-term option. Cirrospilus coachellae Gates (Eulophidae: Eulophinae) is an effective gregarious parasite of peelminer in the Coachella Valley; however, attempts to establish this species in the San Joaquin Valley have so far been unsuccessful. Other natural enemies may be necessary to control peelminer in this region. The discovery of populations of the tetrastichine eulophid Hadrotrichodes waukheon LaSalle parasitizing M. gulosa in the San Joaquin Valley indicates a possible option for biological control of this pest. Hadrotrichodes waukheon (Hymenoptera: Eulophidae: Tetrastichinae) is a parasite of M. gulosa. Newly discovered morphological variations within the species are reported, including the first description of the male. New biological information including preferred life stage of host for parasitism, clutch sizes, male to female ratios and meconial positioning are included. Field studies demonstrated that one to four adult H. waukheon could emerge from a single M. gulosa larva, and later instar M. gulosa larvae were preferred. Hadrotrichodes waukheon is a gregarious, primary parasitoid and may be a candidate agent for biological control of M. gulosa.
7

Estudo de casos de complexidade de colorações gulosa de vértices e de arestas / Case studies of complexity of greedy colorings of vertices and edges

Oliveira, Ana Karolinna Maia de January 2011 (has links)
OLIVEIRA, Ana Karolinna Maia de. Estudo de casos de complexidade de colorações gulosa de vértices e de arestas. 2011. 58 f. : Dissertação (mestrado) - Universidade Federal do Ceará, Centro de Ciências, Departamento de Computação, Fortaleza-CE, 2011. / Submitted by guaracy araujo (guaraa3355@gmail.com) on 2016-05-24T19:36:17Z No. of bitstreams: 1 2011_dis_akmoliveira.pdf: 520341 bytes, checksum: b0c0d48f19d7c3e376c2c79c3a815b08 (MD5) / Approved for entry into archive by guaracy araujo (guaraa3355@gmail.com) on 2016-05-24T19:36:55Z (GMT) No. of bitstreams: 1 2011_dis_akmoliveira.pdf: 520341 bytes, checksum: b0c0d48f19d7c3e376c2c79c3a815b08 (MD5) / Made available in DSpace on 2016-05-24T19:36:55Z (GMT). No. of bitstreams: 1 2011_dis_akmoliveira.pdf: 520341 bytes, checksum: b0c0d48f19d7c3e376c2c79c3a815b08 (MD5) Previous issue date: 2011 / The vertices and edges colorings problems, which consists in determine the smallest number of colors needed to color the vertices and edges of a graph, respectively, so that adjacent vertices and adjacent edges, respectively, have distinct colors, are computationally hard problems and recurring subject of research in graph theory due to numerous practical problems they model. In this work, we study the worst performance of greedy algorithms for coloring vertices and edges. The greedy algorithm has the following general principle: to receive, one by one, the vertices (respect. edges) of the graph to be colored by assigning always the smallest possible color to the vertex (resp. edge) to be colored. We note that so greedy coloring the edges of a graph is equivalent to greedily coloring its line graph, this being the greatest interest in research on greedy edges coloring. The worst performance of the Algorithms is measured by the greatest number of colors they can use. In the case of greedy vertex coloring, this is the number of Grundy or greedy chromatic number of the graph. For the edge coloring, this is the greedy chromatic index or Grundy index of the graph. It is known that determining the Grundy number of any graph is NP-hard. The complexity of determining the Grundy index of any graph was however an open problem. In this dissertation, we prove two complexity results. We prove that the Grundy number of a (q,q−4)-graph can be determined in polynomial time. This class contains strictly the class of cografos P4-sparse for which the same result had been established. This result generalizes so those results. The presented algorithm uses the primeval decomposition of graphs, determining the parameter in linear time. About greedy edge coloring, we prove that the problem of determining the Grundy index is NP-complete for general graphs and polynomial for catepillar graphs, implying that the Grundy number is polynomial for graphs of line of caterpillars. More specifically, we prove that the Grundy index of a caterpillar is D or D+1 and present a polynomial algorithm to determine it exactly. / Os problemas de colorac¸ ˜ao de v´ertices e de arestas, que consistem em determinar o menor n´umero de cores necess´arias para colorir os v´ertices e arestas de um grafo, respectivamente, de forma que v´ertices adjacentes e arestas adjacentes, respectivamente, possuem cores distintas, s˜ao problemas computacionalmente dif´ıceis e s˜ao objeto de pesquisa recorrente em teoria do grafos em virtude de in´umeros problemas pr´aticos que eles modelam. No presente trabalho, estudamos o pior desempenho dos algoritmos gulosos de colorac¸ ˜ao de v´ertices e de arestas. O algoritmo guloso tem o seguinte princ´ıpio geral: receber, um a um, os v´ertices (respect. as arestas) do grafo a ser colorido, atribuindo sempre a menor cor poss´ıvel ao v´ertice (resp. aresta) a ser colorido. Observamos que colorir de forma gulosa as arestas de um grafo equivale a colorir de forma gulosa o seu grafo linha, tendo sido este o maior interesse na pesquisa em colorac¸ ˜ao gulosa de arestas. O pior desempenho dos algoritmos ´e medido pelo maior n´umero de cores que eles podem utilizar. No caso da colorac¸ ˜ao gulosa de v´ertices, esse ´e o n´umero de Grundy ou n´umero crom´atico guloso do grafo. No caso da colorac¸ ˜ao de arestas, esse ´e o ´ındice crom´atico guloso ou ´ındice de Grundy do grafo. Sabe-se que determinar o n´umero de Grundy de um grafo qualquer ´e NP-dif´ıcil. A complexidade de determinar o ´ındice de Grundy de um grafo qualquer era entretanto um problema em aberto. Na presente dissertac¸ ˜ao, provamos dois resultados de complexidade. Provamos que o n´umero de Grundy de um grafo (q,q−4) pode ser determinado em tempo polinomial. Essa classe cont´em estritamente a classe dos cografos e P4-esparsos para os quais o mesmo resultado havia sido estabelecido. Esse resultado generaliza portanto aqueles resultados. O algoritmo apresentado usa a decomposic¸˜ao primeval desses grafos, determinando o parˆametro em tempo linear. No que se refere `a colorac¸ ˜ao de arestas, provamos que o problema de determinar o ´ındice de Grundy ´e NP-completo para grafos em geral e polinomial para grafos caterpillar, implicando que o n´umero de Grundy ´e polinomial para os grafos linha desses. Mais especificamente provamos que o ´ındice de Grundy dos caterpillar ´e D ou D+1 e apresentamos um algoritmo polinomial para determin´a-lo exatamente.

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