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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.
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. See [FGP].
Bibliography
[FGP] Jacob Fox, Andrey Grinshpun and János Pach: The Erdős–Hajnal conjecture for rainbow triangles, J. Combin. Theory, Series B. 111 (2016), 75--125.
* indicates original appearance(s) of problem.
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