Ramsey numbers of paths and graphs of the same order

Chaoping Pei; Yusheng Li

Ramsey numbers of paths and graphs of the same order

Combinatorics 2014-07-29 v1

Authors: Chaoping Pei , Yusheng Li

Abstract

For graphs $F_n$ and $G_n$ of order $n$ , if $R(F_n, G_n)=(\chi(G_n)-1)(n-1)+\sigma(G_n)$ , then $F_n$ is said to be $G_n$ -good, where $\sigma(G_n)$ is the minimum size of a color class among all proper vertex-colorings of $G_n$ with $\chi(G_n)$ colors. Given $\Delta(G_n)\le \Delta$ , it is shown that $P_n$ is asymptotically $G_n$ -good if $\alpha(G_n)\le\frac{n}{4}$ .

Keywords

Ramsey numbers paths graphs of the same order G-good vertex-colorings chromatic number independence number maximum degree

Cite

@article{arxiv.1407.7092,
  title  = {Ramsey numbers of paths and graphs of the same order},
  author = {Chaoping Pei and Yusheng Li},
  journal= {arXiv preprint arXiv:1407.7092},
  year   = {2014}
}

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8 pages, 3 figures

Ramsey numbers of paths and graphs of the same order

Abstract

Keywords

Cite

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