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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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Some topics in Ramsey theoryLaw, Ka-ho., 羅家豪. January 2005 (has links)
published_or_final_version / abstract / Mathematics / Master / Master of Philosophy
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Ramsey-Zahlen für verschiedene GastgebergraphenBode, Jens-Peter January 2007 (has links)
Zugl.: Braunschweig, Techn. Univ., Habil.-Schr., 2007
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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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Some topics in Ramsey theoryLaw, Ka-ho. January 2005 (has links)
Thesis (M. Phil.)--University of Hong Kong, 2005. / Title proper from title frame. Also available in printed format.
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Numbers and topologies two aspects of ramsey theory /Shi, Lingsheng. January 2003 (has links) (PDF)
Berlin, Humboldt-University, Diss., 2003.
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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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Estructura y números de Ramsey para ciclos versus ruedas de tamaño imparSanhueza Matamala, Nicolás Ignacio January 2014 (has links)
Ingeniero Civil Matemático / Se estudia la estructura de grafos completos de tamaño apropiado, con una coloreación de sus aristas en dos colores, de manera tal que no presentan como subgrafos monocromáticos a ciertos tipos de grafos específicos. En este caso se considera el caso de un ciclo impar C_n con n vértices y una rueda W_n := K_1 + C_n con n+1 vértices; en el caso en que n es impar.
Se muestra que para n impar y todo grafo completo de tamaño apropiado, con una coloreación de sus aristas en azul y rojo que no contenga como subgrafo monocromático rojo a C_n ni como subgrafo monocromático azul a W_n; eliminando a lo más dos vértices se obtiene una partición de sus vértices en tres conjuntos que inducen grafos completos de color rojo, y aristas formando un grafo tripartito completo.
Dicho resultado se puede ver como una generalización de resultados presentados por Nikiforov y Schelp; y como una suerte de recíproca a cotas conocidas para números de Ramsey asimétricos.
Como resultado secundario de la demostración se obtienen dos cotas para el número de Ramsey de r(C_{2k+1}, W_{2k+2}): una es más fina para valores pequeños de k y la otra es mejor en el caso asintótico. Los valores exactos de dichos números de Ramsey son, en este instante, un problema abierto. Las cotas expresadas son una aproximación a los valores que han sido conjeturados y permiten ver que, al menos a un nivel asintótico, dichos resultados son ciertos.
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Topics in finite graph Ramsey theoryBorgersen, Robert David 18 January 2008 (has links)
For a positive integer $r$ and graphs $F$, $G$, and $H$, the graph Ramsey arrow notation $F \longrightarrow (G)^H_r$ means that for every $r$-colouring of the subgraphs of $F$ isomorphic to $H$, there exists a subgraph $G'$ of $F$ isomorphic to $G$ such that all the subgraphs of $G'$ isomorphic to $H$ are coloured the same. Graph Ramsey theory is the study of the graph Ramsey arrow and related arrow notations for other kinds of ``graphs" (\emph{e.g.}, ordered graphs, or hypergraphs). This thesis surveys finite graph Ramsey theory, that is, when all structures are finite.
One aspect surveyed here is determining for which $G$, $H$, and $r$, there exists an $F$ such that $F \longrightarrow (G)^H_r$. The existence of such an $F$ is guaranteed when $H$ is complete, whether ``subgraph" means weak or induced, and existence results are also surveyed when $H$ is non-complete. When such an $F$ exists, other aspects are surveyed, such as determining the order of the smallest such $F$, finding such an $F$ in some restricted family of graphs, and describing the set of minimal such $F$'s. / February 2008
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