ARTICLE
Size Ramsey numbers of stars versus cliques
Abstract
The size Ramsey number 
of two graphs 
and 
is the smallest integer 
such that there exists a graph 
on 
edges with the property that every red-blue colouring of the edges of 
yields a red copy of 
or a blue copy of 
. In 1981, Erdős observed that
is sharp. In 1983, Faudree and Sheehan extended this conjecture as follows:
. In 2001, Pikhurko showed that this conjecture is not true for 
and 
, by disproving the mentioned conjecture of Erdős. Here, we prove Faudree and Sheehan's conjecture for a given 
and 
.
