On the Ramsey numbers for a combination of paths and Jahangirs

Details On the Ramsey numbers for a combination of paths and Jahangirs On the Ramsey numbers for a combination of paths and Jahangirs

2007-11-16

arxiv.org/abs/0711.2571v1

Mathematics

Combinatorics

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 improve the Surahmat and Tomescu's result \cite{ST:06} on 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.

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