Highly connected monochromatic subgraphs of multicoloured graphs

Details Highly connected monochromatic subgraphs of multicoloured graphs Highly connected monochromatic subgraphs of multicoloured graphs

2007-02-13

arxiv.org/abs/math/0702354v1

Mathematics

Combinatorics

25 pgs, 3 figures, to appear in Journal of Graph Theory

Scientific paper

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.

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