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Bounds on classical Ramsey numbers.Bannani, Faiz (Faiz Khalil), Carleton University. Dissertation. Mathematics. January 1988 (has links)
Thesis (Ph. D.)--Carleton University, 1989. / Also available in electronic format on the Internet.
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Two new Ramsey numbers /McNamara, James N. January 1992 (has links)
Thesis (M.S.)--Rochester Institute of Technology, 1992. / Typescript. Includes bibliographical references (leaves 36-37).
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Ramsey numbers involving a triangle : theory & algorithms /Jin, Xia. January 1993 (has links)
Thesis (M.S.)--Rochester Institute of Technology, 1993. / Typescript. Includes bibliographical references (leaves 35-38).
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Ramsey Numbers and Two-colorings ofComplete GraphsArmulik, Villem-Adolf January 2015 (has links)
Ramsey theory has to do with order within disorder. This thesis studies two Ramsey numbers, R(3; 3) and R(3; 4), to see if they can provide insight into finding larger Ramsey numbers. The numbers are studied with the help of computer programs. In the second part of the thesis we try to create a coloring of K45 which lacks monochromatic K5 and where each vertex has an equal degree for both color of edges. The results from studying R(3; 3) and R(3; 4) fail to give any further insight into larger Ramsey numbers. Every coloring of K45 we produce contains a monochromatic K5.
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Ramsey NumbersHell, Pavol 11 1900 (has links)
<p> This thesis gives new finite and asymptotic estimates of the Ramsey numbers using certain number-theoretical considerations; it also contains a brief historical survey on determination of Ramsey numbers and related number-theoretical problems.</p> / Thesis / Master of Science (MSc)
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An Extension of Ramsey's Theorem to Multipartite GraphsCook, Brian Michael 04 May 2007 (has links)
Ramsey Theorem, in the most simple form, states that if we are given a positive integer l, there exists a minimal integer r(l), called the Ramsey number, such any partition of the edges of K_r(l) into two sets, i.e. a 2-coloring, yields a copy of K_l contained entirely in one of the partitioned sets, i.e. a monochromatic copy of Kl. We prove an extension of Ramsey's Theorem, in the more general form, by replacing complete graphs by multipartite graphs in both senses, as the partitioned set and as the desired monochromatic graph. More formally, given integers l and k, there exists an integer p(m) such that any 2-coloring of the edges of the complete multipartite graph K_p(m);r(k) yields a monochromatic copy of K_m;k . The tools that are used to prove this result are the Szemeredi Regularity Lemma and the Blow Up Lemma. A full proof of the Regularity Lemma is given. The Blow-Up Lemma is merely stated, but other graph embedding results are given. It is also shown that certain embedding conditions on classes of graphs, namely (f , ?) -embeddability, provides a method to bound the order of the multipartite Ramsey numbers on the graphs. This provides a method to prove that a large class of graphs, including trees, graphs of bounded degree, and planar graphs, has a linear bound, in terms of the number of vertices, on the multipartite Ramsey number.
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Two-Coloring Cycles In Complete GraphsDjang, Claire 11 July 2013 (has links)
No description available.
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R(W₅, K₅)=27 /Stinehour, Joshua. January 2004 (has links)
Thesis (M.S.)--Rochester Institute of Technology, 2004. / Typescript. Includes bibliographical references (leaves 71-75).
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AplicaÃÃes da teoria dos grafos à teoria dos grupos / Applications of graph theory to group theoryMarcelo Mendes de Oliveira 26 February 2008 (has links)
Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / O propÃsito desta dissertaÃÃo à apresentar aplicaÃÃes da Teoria dos Grafos à Teoria dos Grupos. De posse do grafo associado a um grupo finito, nÃs obtemos vÃrios resultados interessantes sobre a estrutura do grupo analisando tal grafo à luz de tÃcnicas-padrÃo da Teoria dos Grafos. Mais precisamente, os nÃmeros cromÃtico e de independÃncia do grafo de um grupo finito nos permitem estimar a cardinalidade mÃxima de um subgrupo abeliano do mesmo, bem
como o tamanho mÃnimo possÃvel de um subconjunto do grupo formado por elementos que nÃo comutam dois a dois; no caso de grupos finitos abelianos, nÃs tambÃm estudamos seus
subconjuntos livres de somas. / This report deals with applications of Graph Theory to Group Theory. Once we construct the graph associated to a finite group, we get several interesting results on the group structure by analysing its associated graph with the help of various standard graph-theoretic tools.
More precisely, the chromatic and independence numbers of the graph of a finite group allows us to estimate the maximal cardinality of an abelian subgroup of it, as well as the minimal size of a subset of the group, all of whose elements donât commute in pairs; for finite abelian
groups, we also study their free-sum subsets.
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Hamiltonicity in Bidirected Signed Graphs and Ramsey Signed NumbersMutar, Mohammed A. January 2017 (has links)
No description available.
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