| Affiliation: | 1. Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran;2. Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran;3. Department of Mathematics, University of Khansar, Khansar, Iran |
| 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 ![urn: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  . |
