Abstract: For positive integers sand t, the Ramsey number is the least positive integer nsuch
that for every graph Gof order n, either Gcontains
as a subgraph or contains as a subgraph. A widely known theorem, proved by Erdös,
states that
In this paper, we improve the upper
bounds for some cases of That is, we have shown that
for
Keywords and phrases: Ramsey numbers, upper bounds, graphs.