Highly connected monochromatic subgraphs of multicoloured graphs
arXiv:math/0702354
Abstract
We consider the following question of Bollobas: given an r-colouring of the edges of the complete graph on n vertices, how large a k-connected subgraph can we find using only one colour? We solve this problem asymptotically when r-1 is a prime power, and exactly for 2- and 3-colourings.
25 pgs, 3 figures, to appear in Journal of Graph Theory