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The Ramsey Numbers of Paths Versus Kipases by A.N.M. Salman; H.J. Broersma is a Computer Science article available to read on EtoBox.

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For two given graphs G and H, the Ramsey number R(G, H) is the smallest positive integer p such that for every graph F on p vertices the following holds: either F contains G as a subgraph or the complement of F contains H as a subgraph. In this paper, we study the Ramsey numbers R(Pn, Km), where Pn is a path on n vertices and Km is the graph obtained from the join of K1 and Pm. We determine the exact values of R(Pn, Km) for the following values of n and m: 1 ≤ n ≤ 5 and m ≥ 3; n ≥ 6 and (m is odd, 3 ≤ m ≤ 2n -1) or (m is even, 4 ≤ m ≤ n + 1); n = 6 or 7 and m = 2n -2 or m ≥ 2n; n ≥ 8 and m = 2n -2 or m = 2n or (q • n -2q + 1 ≤ m ≤ q • n -q + 2 with 3 ≤ q ≤ n -5) or m ≥ (n -3) 2 ; odd n ≥ 9 and (q • n -3q + 1 ≤ m ≤ q • n -2q with 3 ≤ q ≤ (n -3)/2) or (q • n -q -n + 4 ≤ m ≤ q • n -2q with (n -1)/2 ≤ q ≤ n -4).

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Author

A.N.M. Salman; H.J. Broersma

Publisher

Elsevier Science; Elsevier ; Elsevier BV; Amsterdam: Elsevier BV (ISSN 1571-0653)

Published

2004

Language

EN

Field

Computer Science (Physical Sciences)