THE RAMSEY NUMBERS FOR DISJOINT UNION OF STARS
Abstract: The Ramsey number
for a graph G versus a graph H, denoted by R(G; H), is the smallest positive
integer n such that for any graph F of order n,either F contains G as a
subgraph or F contains H as a subgraph. In this paper, we investigate the
Ramsey numbers for union of stars versus small cycle and small wheel. We show
that if ni ≥ 3 for i = 1; 2; : : : ; k and ni ≥ ni+1 ≥ pni − 2, then R(Sk i=1
S1+ni; C4) = Pk i=1 ni + k + 1 for k ≥ 2. Furthermore, we show that if ni is
odd and 2ni+1 ≥ ni for every i, then R(Sk i=1 Sni; W4) = R(Snk; W4) + Pk i=1 −1
ni for k ≥ 1:
Author: Hasmawati
Journal Code: jpmatematikagg100014
