American Statistical Association (K5)

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R(C6, K5) = 21andR(C7, K5) = 25

R(C4, K4) = 10 (see [2]) R(C4, K5) = 14 (see [3]) R(C5, K4) = 13, R(C5, K5) = 17 (see [5, 6]) R(Cn, K3) = 2n − 1 (n > 3) (see [4, 7]). In [10], we proved that R(Cn, K4) = 3(n − 1) + 1 (n ≥ 4). In this paper, we will prove that R(Cn, K5) = 4(n − 1)+ 1 (n = 6, 7). The following notations will be used in this paper. If G is a graph, the vertex set (resp. edge set) of G is denoted by V (G) (resp. E...

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For two given graphs G1 and G2, the Ramsey number r(G1, G2) is the smallest integer n such that for any graph G of order n, either G contains G1 or the complement of G contains G2. Let Km denote a complete graph of order m and Kn −P3 a complete graph of order n without two incident edges. In this paper, we prove that r(K5 − P3,K5) = 25 without help of computer algorithms.

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ژورنال

عنوان ژورنال: Science

سال: 1958

ISSN: 0036-8075,1095-9203

DOI: 10.1126/science.127.3295.419