By a wild colouring we shall mean an edge colouring f of a graph with the property that for all vertex colourings g there is a colour class in which f assumes all values. Trivially, in order for such colourings to exist one has to work with the right number of colours for f (we shall think of this as kappa^+) and g (we shall deal with kappa here) and restrict one's attention to graphs with a sufficiently large chromatic number (kappa^+) (other choices for these cardinals are possible). Continuing the research of Hajnal and Komjath who among other results studied such colourings for kappa regular, we present some results from work in progress with Komjath and Morgan about the situation when kappa is singular.
Copyright M. Dzamonja