On path-quasar Ramsey numbers
نویسنده
چکیده
Let G1 and G2 be two given graphs. The Ramsey number R(G1, G2) is the least integer r such that for every graph G on r vertices, either G contains a G1 or G contains a G2. Parsons gave a recursive formula to determine the values of R(Pn,K1,m), where Pn is a path on n vertices and K1,m is a star on m+1 vertices. In this note, we study the Ramsey numbers R(Pn,K1 ∨Fm), where Fm is a linear forest on m vertices. We determine the exact values of R(Pn,K1 ∨ Fm) for the cases m ≤ n and m ≥ 2n, and for the case that Fm has no odd component. Moreover, we give a lower bound and an upper bound for the case n+1 ≤ m ≤ 2n− 1 and Fm has at least one odd component.
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