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arXiv · 1710.06383

Projective planes and set multipartite Ramsey numbers for $C_4$ versus star

Claudia J. F. Gonçalves·Emerson L. Monte Carmelo·Irene N. Nakaoka
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Abstract

Set multipartite Ramsey numbers were introduced in 2004, ge-neralizing the celebrated Ramsey numbers. Let $C_4$ denote the four cycle and let $K_{1,n}$ denote the star on $n+1$ vertices. In this paper we investigate bounds on $C_4-K_{1,n}$ set multipartite Ramsey numbers. Relationships between these numbers and the classical $C_4-K_{1,n}$ 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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Claudia J. F. Gonçalves, Emerson L. Monte Carmelo, Irene N. Nakaoka. 2017-10-17. Projective planes and set multipartite Ramsey numbers for $C_4$ versus star. https://arxiv.org/abs/1710.06383

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