Abstract

For graphs G and H, the Ramsey number R(G,H) is the least integer n such that every 2-coloring of the edges of K_n contains a subgraph isomorphic to G in the first color or a subgraph isomorphic to H in the second color. Graph G is a (C_4, K_n)-graph if G doesn't contain a cycle C_4 and G has no independent set of order n. Jayawardene and Rousseau showed that 21 <= R(C_4,K_7) <= 22. In this work we determine R(C_4, K_7) = 22 and R(C_4,K_8) = 26, and enumerate various families of (C_4, K_n)-graphs. In particular, we construct all (C_4, K_n)-graphs for n < 7, and all (C_4,K_7)-graphs on at least 19 vertices. Most of the results are based on computer algorithms.

Publication Date

2002

Comments

ISSN:0835-3026 Note: imported from RIT’s Digital Media Library running on DSpace to RIT Scholar Works in February 2014.

Document Type

Article

Department, Program, or Center

Center for Advancing the Study of CyberInfrastructure

Campus

RIT – Main Campus

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