On Ramsey number for tree versus kipas graph of odd order Intan Sherlin (a), Suhadi Wido Saputro (b), Edy Tri Baskoro (b,c*)
(a) Doctoral Program of Mathematics, Faculty of Mathematics and Natural Sciences,
Institut Teknologi Bandung, Indonesia
30121002[at]mahasiswa.itb.ac.id
(b) Combinatorial Mathematics Research Group, Faculty of Mathematics and Natural Sciences,
Institut Teknologi Bandung, Indonesia
suhadi[at]itb.ac.id
(c) Center for Research Collaboration on Graph Theory and Combinatorics, Indonesia
*ebaskoro[at]itb.ac.id
Abstract
Given two graphs G and H, the graph Ramsey number R(G, H) is the least natural number r such that for every graph F on r vertices, either F contains a copy of G or \overline{F} contains a copy of H. A vertex v is called a dominating vertex in a graph G if it is adjacent to all other vertices of G. A wheel W_n is a graph consisting one dominating vertex and n other vertices forming a cycle. A kipas F_{1,m} is a fan graph formed from a wheel W_n by removing one cycle-edge. In this paper, we consider the graph Ramsey number of a tree T_n and a kipas F_{1,m}. The study of R(T_n,F_{1,m}) has been initiated by Li et. al. (2016) where T_n is a star. This paper will give the graph Ramsey numbers for T_n is not a star versus kipas F_{1,m} with m=4, 6, and 8.
Keywords: graph Ramsey number, Ramsey number tree versus kipas
