Multipartite Ramsey numbers for odd cycles
نویسندگان
چکیده
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, ∗2000 Mathematics Subject Classification: 05C55, 05C38. †Research supported in part by the National Science Foundation under Grant No. DMS-0456401.
منابع مشابه
A multipartite Ramsey number for odd cycles
In this paper we study multipartite Ramsey numbers for odd cycles. Our main result is the proof of a conjecture of Gyárfás, Sárközy and Schelp [12]. Precisely, 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 cycle of length n. keywords: cycles, Ramsey number, Regular...
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عنوان ژورنال:
- Journal of Graph Theory
دوره 61 شماره
صفحات -
تاریخ انتشار 2009