The connected size Ramsey number for pair of matchings and small paths
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The connected size Ramsey number of a graph G and H, denoted by ^rc(G;H) is the smallest integer ^rc such that there is a connected graph F of ^rc edges with the property that any red-blue coloring of the edges of F yields either a red subgraph G or a blue subgraph H: In this paper, we consider the connected size Ramsey number for a pair of a matching and a path. In particular, we derive an upper bound of ^rc(tK2; Pn) for n; t 2: We also determine the exact values of ^rc(tK2; Pn); for some xed n and t:
Abstract
The connected size Ramsey number of a graph G and H, denoted by ^rc(G;H) is the smallest integer ^rc such that there is a connected graph F of ^rc edges with the property that any red-blue coloring of the edges of F yields either a red subgraph G or a blue subgraph H: In this paper, we consider the connected size Ramsey number for a pair of a matching and a path. In particular, we derive an upper bound of ^rc(tK2; Pn) for n; t 2: We also determine the exact values of ^rc(tK2; Pn); for some xed n and t:
참고문헌 (10)
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