Planar Ramsey Numbers of Four Cycles Versus Wheels

2013/04/24 by Chen Yaojun, Yaojun, Chen, Miao Zhengke +3
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.1304.6466

arxiv created 2013/04/24 · arxiv updated 2013/04/25

Abstract

For two given graphs G and H the planar Ramsey number PR(G,H) is the smallest integer n such that every planar graph F on n vertices either contains a copy of G, or its complement contains a copy of H. In this paper, we first characterize some structural properties of C₄-free planar graphs, and then we determine all planar Ramsey numbers PR(C₄, W_n), for n≥ 3.

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