Abstract
AbstractThe 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 thaturn:x-wiley:03649024:media:jgt22453:jgt22453-math-0010 and he conjectured that this upper bound on is sharp. In 1983, Faudree and Sheehan extended this conjecture as follows:urn:x-wiley:03649024:media:jgt22453:jgt22453-math-0012 They proved the case . 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 .
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