A Random Recolouring Method for Graphs and Hypergraphs

We consider a simple randomised algorithm that seeks a weak 2-colouring of a hypergraph H ; that is, it tries to 2-colour the points of H so that no edge is monochromatic. If H has a particular well-behaved form of such a colouring, then the method is successful within expected number of iterations O ( n 3 ) when H has n points. In particular, when applied to a graph G with n nodes and chromatic number 3, the method yields a 2-colouring of the vertices such that no triangle is monochromatic in expected time O ( n 4 ).