Centre for Discrete and Applicable Mathematics |
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CDAM Research Report, LSE-CDAM-2006-06May 2006 |
Unions of Perfect Matchings in Cubic Graphs and Implications of the Berge-Fulkerson Conjecture
Viresh Patel
The Berge-Fulkerson Conjecture states that every cubic bridgeless graph has six perfect matchings such that every edge of the graph is in exactly two of the perfect matchings. If the Berge-Fulkerson Conjecture is true, then what can we say about the proportion of edges of a cubic bridgeless graph that can be covered by k of its perfect matchings? This is the question we address in this paper. We then give a possible method for proving, independently of the Berge-Fulkerson Conjecture, the bounds obtained.A PDF file (130 kB) with the full contents of this report can be downloaded by clicking here.
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