AUTHOR=Li Xiangmei , Fahad Asfand , Zhou Xiaoqing , Yang Hong TITLE=Exact Values for Some Size Ramsey Numbers of Paths and Cycles JOURNAL=Frontiers in Physics VOLUME=8 YEAR=2020 URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2020.00350 DOI=10.3389/fphy.2020.00350 ISSN=2296-424X ABSTRACT=

For the graphs G₁, G₂, and G, if every 2-coloring (red and blue) of the edges of G results in either a copy of blueG₁ or a copy of redG₂, we write G → (G₁, G₂). The size Ramsey number R^(G1,G2) is the smallest number e such that there is a graph G with size e satisfying G → (G₁, G₂), i.e., R^(G1,G2)=min{|E(G)|:G→(G1,G2)}. In this paper, by developing the procedure and algorithm, we determine exact values of the size Ramsey numbers of some paths and cycles. More precisely, we obtain that R^(C4,C5)=19, R^(C6,C6)=26, R^(P4,C5)=14, R^(P4,P5)=10, R^(P4,P6)=14, R^(P5,P5)=11, R^(P3,P5)=7 and R^(P3,P6)=8.