The Cost of Perfection for Matchings in Graphs

Details The Cost of Perfection for Matchings in Graphs The Cost of Perfection for Matchings in Graphs

2012-04-11

arxiv.org/abs/1204.2727v1

Computer Science

Discrete Mathematics

Scientific paper

Perfect matchings and maximum weight matchings are two fundamental combinatorial structures. We study the relationship between these two structures. More precisely, we consider the ratio between the maximum weight of a perfect matching and the maximum weight of a general matching. First, we characterize graphs that attain the extreme ratios. Second, we present tight bounds for this ratio on the class of Tait-colorable cubic graphs. Finally, we consider the class of bridgeless cubic graphs, relating the Berge-Fulkerson conjecture with the aforementioned ratio.

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