Conjecture   For every fixed and fixed colouring of with colours, there exists such that every colouring of the edges of contains either vertices whose edges are coloured according to or vertices whose edges are coloured with at most colours.

Problem   Does there exist a graph with no subgraph isomorphic to which cannot be expressed as a union of triangle free graphs?

Conjecture   For every fixed graph , there exists a constant , so that every graph without an induced subgraph isomorphic to contains either a clique or an independent set of size .