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The connected size Ramsey number for pair of matchings and small paths
BUDI RAHADJENG,HILDA ASSIYATUN,EDY TRI BASKORO 장전수학회 2019 Proceedings of the Jangjeon mathematical society Vol.22 No.1
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: