1 7 O ct 2 01 7 Projective planes and set multipartite Ramsey numbers for C 4 versus star Claudia
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چکیده
Set multipartite Ramsey numbers were introduced in 2004, generalizing the celebrated Ramsey numbers. Let C4 denote the four cycle and let K1,n denote the star on n + 1 vertices. In this paper we investigate bounds on C4−K1,n set multipartite Ramsey numbers. Relationships between these numbers and the classical C4−K1,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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تاریخ انتشار 2017