The Ramsey number r(K5 - P3,K5)

Description

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 comple ment 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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