Abstract
The multicolor Ramsey number R r (H) is defined to be the smallest integer n=n(r) with the property that any r-coloring of the edges of the complete graph K n must result in a monochromatic subgraph of K n isomorphic to H. It is well known that 2rm<R r (C2 m +1)<2(r+2)!m and R r (C2 m )≥(r−1)(m−1)+1. In this paper, we prove that R r (C2 m )≥2(r−1)(m−1)+2.
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This research is supported by NSFC(60373096, 60573022) and SRFDP(20030141003)
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Yongqi, S., Yuansheng, Y., Feng, X. et al. New Lower Bounds on the Multicolor Ramsey Numbers R r (C2 m ). Graphs and Combinatorics 22, 283–288 (2006). https://doi.org/10.1007/s00373-006-0659-y
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DOI: https://doi.org/10.1007/s00373-006-0659-y