On Ramsey Minimal Graphs For (P4,Pn), For n≥5

Nailul Yuni Permataputri, Lyra Yulianti, Des Welyyanti

Abstract


For given two graphs G and H, the notation F \righttarrow (G,H) means that any red-blue coloring of all the edges of F contains a red copy of G as a subgraph or a blue copy of H as a subgraph. A graph F is Ramsey (G,H)-minimal if F \righttarrow (G,H)  and for any edge e in F then  F-e  \nrighttarrow (G,H). The class of all (G,H)-minimal graph, is denoted by \mathcal{R}(G,H). In this paper, some graph in  \mathcal{R}(P_4,P_5) are obtained. Then, a graph in \mathcal{R}(P_4,P_n)  for even n,  n>=6 and a graph in \mathcal{R}(P_4,P_n) for odd n, n>=7 is also obtained.

Keywords


Ramsey minimal graph; path graph; cycle graph; complete graph

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DOI: http://dx.doi.org/10.52155/ijpsat.v37.1.5102

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