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2006•Unpublished venueRequires access

Unions of Perfect Matchings in Cubic Graphs and Implications of the Berge-Fulkerson Conjecture

Viresh Patel

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Abstract

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. 1

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What this paper is about

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. 1

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Available abstract

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. 1

Key concepts: Cubic graph, Combinatorics, Trivially perfect graph, Perfect graph theorem, Strong perfect graph theorem, Conjecture, Mathematics, Perfect graph

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