Lower bounds for Ramsey numbers and association schemes (Q1084415)

The Ramsey number \(r_ n(k)\) is the least positive integer so that any k-coloring of the complete graph on that number of vertices admits a monochromatic complete subgraph on k-vertices. In this paper the authors introduces some new constructions, based on association schemes, which give improvements in the known lower-bound for \(r_ 3(k)\). Some of the specific bounds computed are: \(r_ 2(7)\geq 205\); \(r_ 2(9)\geq 565\), \(r_ 2(10)\geq 798\), \(r_ w(11)\geq 1597\), \(r_ 3(14)\geq 128\) \(r_ 3(5)\geq 385\), \(r_ 3(6)\geq 727\), \(r_ 3(7)\geq 3211\), \(r_ 4(4)\geq 458\), \(r_ 4(5)\geq 1833\), \(r_ 4(6)\geq 3433\), \(r_ 4(7)\geq 12841\), \(r_ 5(5)\geq 4711\).