Using Partitioning Graphs to Calculate Some Ramsey Numbers

Abstract:

Ramsey number is the smallest integer N such that for any redblue edgecoloring of KN, there is a red subgraph G or a blue subgraph H. In this paper, we use a theorem of Burr and the method of partitioning graphs to prove that if n≥|G|2+2χ(G)α(G), then R(Pn,G)=(χ(G)－1)(n－1)+σ(G).