Let $G_1$ and $G_2$ be two given graphs. The Ramsey number $R(G_1,G_2)$ is the least integer $r$ such that for every graph $G$ on $r$ vertices, either $G$ contains a $G_1$ or $\overline{G}$ contains a $G_2$. We denote by $P_n$ the path on $n$ vertices and $W_m$ the wheel on $m+1$ vertices. Chen et al. and Zhang determined the values of $R(P_n,W_m)$ when $m\leq n+1$ and when $n+2\leq m\leq 2n$, respectively. In this paper we determine all the values of $R(P_n,W_m)$ for the left case $m\geq 2n+1$. Together with Chen et al.'s and Zhang's results, we give a complete solution to the problem of determining the Ramsey numbers of paths versus wheels.
@article{10_37236_3968,
author = {Binlong Li and Bo Ning},
title = {The {Ramsey} numbers of paths versus wheels: a complete solution},
journal = {The electronic journal of combinatorics},
year = {2014},
volume = {21},
number = {4},
doi = {10.37236/3968},
zbl = {1305.05140},
url = {http://geodesic.mathdoc.fr/articles/10.37236/3968/}
}
TY - JOUR
AU - Binlong Li
AU - Bo Ning
TI - The Ramsey numbers of paths versus wheels: a complete solution
JO - The electronic journal of combinatorics
PY - 2014
VL - 21
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/3968/
DO - 10.37236/3968
ID - 10_37236_3968
ER -
%0 Journal Article
%A Binlong Li
%A Bo Ning
%T The Ramsey numbers of paths versus wheels: a complete solution
%J The electronic journal of combinatorics
%D 2014
%V 21
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/3968/
%R 10.37236/3968
%F 10_37236_3968
Binlong Li; Bo Ning. The Ramsey numbers of paths versus wheels: a complete solution. The electronic journal of combinatorics, Tome 21 (2014) no. 4. doi: 10.37236/3968
