In this paper we study multipartite Ramsey numbers for odd cycles. We formulate the following conjecture: Let n ¸ 5 be an arbitrary positive odd integer, then in any two-coloring of the edges of the complete 5-partite graph K((n ¡ 1)=2; (n ¡ 1)=2; (n ¡ 1)=2; (n ¡ 1)=2; 1) there is a monochromatic Cn, a cycle of length n. This roughly says that the Ramsey number for Cn (i.e. 2n¡1) will not change (somewhat surprisingly) if four large \holes" are allowed. Note that this would be best possible as the statement is not true if we delete from K2n¡1 the edges within a set of size (n + 1)=2. We prove an approximate version of the above conjecture.
, Sárközy, Gábor N.
, Schelp, Richard H.
(2008). Multipartite Ramsey numbers for odd cycles. .
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