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On 1-dependent ramsey numbers for graphs
Discussiones Mathematicae Graph Theory
A set X of vertices of a graph G is said to be 1-dependent if the subgraph of G induced by X has maximum degree one. The 1-dependent Ramsey number t 1 (l, m) is the smallest integer n such that for any 2-edge colouring (R, B) of K n , the spanning subgraph B of K n has a 1-dependent set of size l or the subgraph R has a 1-dependent set of size m. The 2-edge colouring (R, B) is a t 1 (l, m) Ramsey colouring of K n if B (R, respectively) does not contain a 1-dependent set of size l (m,doi:10.7151/dmgt.1088 fatcat:e3jz5u237be2nj4ny4uzfawov4