منابع مشابه
Three-Color Ramsey Numbers For Paths
We prove for sufficiently large n the following conjecture of Faudree and Schelp : R(Pn, Pn, Pn) = { 2n− 1 for odd n, 2n− 2 for even n, for the three-color Ramsey numbers of paths on n vertices. ∗2000 Mathematics Subject Classification: 05C55, 05C38. The second author was supported in part by OTKA Grants T038198 and T046234.
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For graphs G1, G2, G3, the three-color Ramsey number R(G1, G2, G3) is the smallest integer n such that if we arbitrarily color the edges of the complete graph of order n with 3 colors, then it contains a monochromatic copy of Gi in color i, for some 1 ≤ i ≤ 3. First, we prove that the conjectured equality R3(C2n, C2n, C2n) = 4n, if true, implies that R3(P2n+1, P2n+1, P2n+1) = 4n + 1 for all n ≥...
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ژورنال
عنوان ژورنال: Graphs and Combinatorics
سال: 2015
ISSN: 0911-0119,1435-5914
DOI: 10.1007/s00373-014-1507-0