On the Ramsey numbers for paths and generalized Jahangir graphs

Details On the Ramsey numbers for paths and generalized Jahangir graphs On the Ramsey numbers for paths and generalized Jahangir graphs

2008-05-10

arxiv.org/abs/0805.1455v1

Mathematics

Combinatorics

6 pages

Scientific paper

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 $R(tP_n,H)$, where $H$ is a generalized Jahangir graph $J_{s,m}$ where $s\geq2$ is even, $m\geq3$ and $t\geq1$ is any integer.

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