On size Ramsey number of paths, trees, and circuits. I

Abstract

AbstractThe size Ramsey number ř(G) of a graph G is the smallest integer ř such that there is a graph F of ř edges with the property that any two‐coloring of the edges of F yields a monochromatic copy of G. First we show that the size Ramsey number ř(Pn) of the path Pn of length n is linear in n, solving a problem of Erdös. Second we present a general upper bound on size Ramsey numbers of trees.