2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/123900We 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 TheoryCombinatoricstext