On the Ramsey numbers for paths and generalized Jahangir graphs

Abstract

For given graphs $G$ and $H,$ the \emph{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 determine the Ramsey number of paths versus generalized Jahangir graphs. We also derive the Ramsey number $R(t{P}_n,H)$, where $H$ is a generalized Jahangir graph $J_{s,m}$ where $s\ge 2$ is even, $m\ge 3$ and $t\ge 1$ is any integer.

6 pages