Kashif Ali, E. T. Baskoro, Ioan Tomescu: On the Ramsey numbers for paths and generalized Jahangir graphs $J_{s,m}$, p.177-182

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 determine the Ramsey number of paths versus generalized Jahangir graphs. We also derive the Ramsey number $R(tP_n,H)$, where $H$ is a generalized Jahangir graph $J_{s,m}$ where $s\geq2$ is even, $m\geq3$ and $t\geq1$ is any integer.

Key Words: Ramsey number, path, generalized Jahangir graph.

2000 Mathematics Subject Classification: Primary: 05C55,
Secondary: 05D10.

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