New upper bound for multicolor Ramsey number of odd cycles
نویسندگان
چکیده
منابع مشابه
New Lower Bound for Multicolor Ramsey Numbers for Even Cycles
For given finite family of graphs G1, G2, . . . , Gk, k ≥ 2, the multicolor Ramsey number R(G1, G2, . . . , Gk) is the smallest integer n such that if we arbitrarily color the edges of the complete graph on n vertices with k colors then there is always a monochromatic copy of Gi colored with i, for some 1 ≤ i ≤ k. We give a lower bound for k−color Ramsey number R(Cm, Cm, . . . , Cm), where m ≥ ...
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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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Let G1, G2, . . . , Gt be graphs. The multicolor Ramsey number R(G1, G2, . . . , Gt) is the smallest positive integer n such that if the edges of a complete graph Kn are partitioned into t disjoint color classes giving t graphs H1,H2, . . . ,Ht, then at least one Hi has a subgraph isomorphic to Gi. In this paper, we provide the exact value of R(Pn1 , Pn2 , . . . , Pnt , Ck) for certain values o...
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For given graphs G1, G2, . . . , Gk, k ≥ 2, the multicolor Ramsey number R(G1, G2, . . . , Gk) is the smallest integer n such that if we arbitrarily color the edges of the complete graph on n vertices with k colors, then it is always a monochromatic copy of some Gi, for 1 ≤ i ≤ k. We give a lower bound for k-color Ramsey number R(Cm, Cm, . . . , Cm), where m ≥ 8 is even and Cm is the cycle on m...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2019
ISSN: 0012-365X
DOI: 10.1016/j.disc.2018.09.014