@book{67361ed0b22b4216a85645d1795f0ff4,

title = "The Ramsey numbers of large star-like trees versus large odd wheels",

abstract = "For two given graphs $G$ and $H$, the \textit{Ramsey number} $R(G,H)$ is the smallest positive integer $N$ such that for every graph $F$ of order $N$ the following holds: either $F$ contains $G$ as a subgraph or the complement of $F$ contains $H$ as a subgraph. In this paper, we shall study the Ramsey number $R(T_n,W_{m})$ for a star-like tree $T_n$ with $n$ vertices and a wheel $W_m$ with $m+1$ vertices and $m$ odd. We show that the Ramsey number $R(S_{n},W_{m})=3n-2 $ for $n\geq 2m-4, m\geq 5$ and $m$ odd, where $S_n$ denotes the star on $n$ vertices. We conjecture that the Ramsey number is the same for general trees on $n$ vertices, and support this conjecture by proving it for a number of star-like trees.",

keywords = "MSC-05C55, IR-65808, EWI-3441, MSC-05D10",

author = "Surahmat and E.T. Baskoro and H.J. Broersma",

note = "Imported from MEMORANDA",

year = "2002",

language = "English",

series = "Memorandum",

publisher = "University of Twente, Department of Applied Mathematics",

number = "1621",

}