Connected Size Ramsey Numbers for Matchings versus Cycles or Paths

Let F, G, and H be finite, simple and undirected graphs. The connected size Ramsey number (r) over cap (c)(G, H) of graph G and H is the least integer k such that there is a connected graph F with k edges and if the edge set of F is arbitrarily colored by red or blue, then there always exists either a red copy of G or a blue copy of H. In this paper, we determine the connected size Ramsey number (r) over cap (c)(2K(2), C-n), for n >= 4, an upper bound of (r) over cap (c)(nK(2), P-4), for n >= 2, and the exact value of (r) over cap (c)(nK(2), P-4), for 2 <= n <= 5. (C) 2015 The Authors. Published by Elsevier B.V.