The theta-complete graph Ramsey number R(θn K5) = 4n - 3 for n = 6 and n≥ 10

Abstract

For any two graphs F1 and F2, the graph Ramsey number r(F1, F2) is the smallest positive integer N with the property that every graph of at least N vertices contains F1 or its complement contains F2 as a subgraph. In this paper, we consider the Ramsey numbers for theta-complete graphs. In fact, we prove that r(θn, K5) = 4n-3 for n = 6 and n ≥.