An improved linear bound on the number of perfect matchings in cubic graphs
classification
🧮 math.CO
keywords
perfectboundcubicmatchingsbridgelessconstantdiffersdimension
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We show that every cubic bridgeless graph with n vertices has at least 3n/4-10 perfect matchings. This is the first bound that differs by more than a constant from the maximal dimension of the perfect matching polytope.
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