On induced Ramsey numbers Original Research Article

The induced Ramsey number IR(G,H) is defined as the smallest integer n, for which there exists a graph F on n vertices such that any 2-colouring of its edges with red and blue leads to either a red copy of G induced in F, or an induced blue H. In this note, we study the value of the induced Ramsey numbers, as well as their planar and weak versions, for some special classes of graphs. In particular, we show that, for the induced planar Ramsey numbers, the fact whether we prohibit monochromatic copies induced in the graph, or induced just in its own colour, may significantly affect the value of the Ramsey number.