A Remark on Star-C4 and Wheel-C4 Ramsey Numbers

Yanbo Zhang • Hajo Broersma • Yaojun Chen

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(English, 5 pages)

Abstract

Given two graphs G1 and G2, the Ramsey number R(G1;G2)is the smallest integer N such that, for any graph G of order N, either G1 is a subgraph of G, or G2 is a subgraph of the complement of G. Let Cn denote a cycle of order n, Wn a wheel of order n+1 and Sn a star of order n. In this paper, it is shown that R(Wn;C4) = R(Sn+1;C4) for n ≥ 6. Based on this result and Parsons' results on R(Sn+1;C4), we establish the best possible general upper bound for R(Wn;C4) and determine some exact values for R(Wn;C4).

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Journal

Electronic Journal of Graph Theory and Applications

The Electronic Journal of Graph Theory and Applications (EJGTA) is a refereed journal devoted to ... see more