On the Ramsey Numbers for a Combination of Paths and Jahangirs

Abstract

For given graphs $G$ and $H$, the Ramsey number $R(G,H)$ is the least natural number $n$ such that for every graph $F$ of order $n$ the following condition holds: either $F$ contains $G$ or the complement of $F$ contains $H$. In this paper, we improve the Ramsey number of paths versus Jahangirs. We also determine the Ramsey number $R(\cup G,H)$, where $G$ is a path and $H$ is a Jahangir graph.