Highly connected monochromatic subgraphs of multicoloured graphs
Henry Liu, Robert Morris, Noah Prince
TL;DR
This paper investigates the maximum size of monochromatic, highly connected subgraphs in multicoloured complete graphs, providing asymptotic solutions for prime power colourings and exact results for two and three colours.
Contribution
It offers the first asymptotic solution for the problem when the number of colours minus one is a prime power, and exact solutions for two- and three-colour cases.
Findings
Asymptotic bounds established for prime power colourings.
Exact maximum sizes determined for 2- and 3-colourings.
Advances understanding of monochromatic connectivity in multicoloured graphs.
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.
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Taxonomy
TopicsLimits and Structures in Graph Theory