Projective planes and set multipartite Ramsey numbers for C₄ versus star

2017/10/17 by Gonçalves, Claudia J. F., Carmelo, Emerson L. Monte, Nakaoka, Irene N.
#05B25 #05C55 #05D10 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1710.06383

Abstract

Set multipartite Ramsey numbers were introduced in 2004, ge-neralizing the celebrated Ramsey numbers. Let C₄ denote the four cycle and let K_1,n denote the star on n+1 vertices. In this paper we investigate bounds on C₄-K_1,n set multipartite Ramsey numbers. Relationships between these numbers and the classical C₄-K_1,n Ramsey numbers are explored. Then several near-optimal or exact classes are derived as applications. As the main goal, polarity graphs from projective planes allow us to find suitable subgraphs which yield some optimal classes too.

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