2015/11/25 by Haghi, Sh., Maimani, H. R., Seify, A.
#05C55 #05D10 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1511.08163
For two graphs G and H, the Ramsey number r(G,H) is the smallest positive integer r, such that any red/blue coloring of the edges of the graph Kr contains either a red subgraph that is isomorphic to G or a blue subgraph that is isomorphic to H. Let Sk=K1,k be a star of order k+1 and Kn\sqcup Sk be a graph obtained from Kn by adding a new vertex v and joining v to k vertices of Kn. The star-critical Ramsey number r_*(G,H) is the smallest positive integer k such that any red/blue coloring of the edges of graph Kr-1\sqcup Sk contains either a red subgraph that is isomorphic to G or a blue subgraph that is isomorphic to H, where r=r(G,H). In this paper, it is shown that r_*(Fn,K4)=4n+2, where n≥4.