| Ramsey theory is a large and beautiful area of combinatorics and graph theory. It expresses the deep mathematical principle that no matter how the objects of a 'large' structure are partitioned into a 'few' classes, one of these classes contains a 'large' subsystem. As an important research direction of Ramsey theory, Ramsey numbers not only have great theoretical significance, but also may be applied to computer science, communications, decision-making, and so on. But the determination of Ramsey numbers is a No-Polynomial Problem, only a few of exact values have been obtained.If there exists a r - coloring of the edges of a complete graph KR such that there is no monochromatic subgragh of KR isomorphic to H, we say that KR is r-colorable to forbidden subgraph H. The multicolor Ramsey number Rr (H) is defined to be the smallest integer R such that KR is not r - colorable to H.The Ramsey number Rr (H) is studied in this paper, where the graph H is a cycle.Ronald L. Graham, Burce L. Rothschild and Joel H. Spencer, (Ramsey Theory, Second Edition, JOHN WILEY & SONS, 1990) proved:Using factorization, a new lower bound formula is obtained:If r = 3, this paper determines that R3(C8) = 16. Furthermore, this paper conjectures that... |
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