期刊名称：AKCE International Journal of Graphs and Combinatorics
印刷版ISSN：0972-8600
出版年度：2018
卷号：15
期号：2
页码：174-186
DOI：10.1016/j.akcej.2017.08.003
语种：English
出版社：Elsevier
摘要：AbstractLetF,G,andHbe simple graphs. We writeF→(G,H)to mean that any red–blue coloring of all edges ofFwill contain either a red copy ofGor a blue copy ofH.A graphF(without isolated vertices) satisfyingF→(G,H)and for eache∈E(F),(F−e)↛(G,H)is called a Ramsey(G,H)-minimal graph. The set of all Ramsey(G,H)-minimal graphs is denoted byℛ(G,H).In this paper, we derive the necessary and sufficient condition of graphs belonging toℛ(4K2,H),for any connected graphH.Moreover, we give a relation between Ramsey(4K2,P3)- and(3K2,P3)-minimal graphs, and Ramsey(4K2,P3)- and(2K2,P3)-minimal graphs. Furthermore, we determine all graphs inℛ(4K2,P3).
