The theta-complete graph Ramsey number r(θk, K5); k = 7, 8, 9

Abstract

Finding the Ramsey number is an important problem of the well-known family of the combinatorial problems in Ramsey theory. In this work, we investigate the Ramsey number r(θs, K5) for s = 7, 8, 9 where θs is the set of theta graphs of order s and K5 is a complete graph of order 5. Our result closed the problem of finding R(θs, K5) for each s ≥ 6.