Upper Bounds for Perfect Matchings in Pfaffian and Planar Graphs

Afshin Behmaram, Shmuel Friedland


We give upper bounds on weighted perfect matchings in Pfaffian graphs. These upper bounds are better than Bregman's upper bounds on the number of perfect matchings. We show that some of our upper bounds are sharp for 3 and 4-regular Pfaffian graphs. We apply our results to fullerene graphs.


Perfect matchings, pfaffian graphs, fullerene graphs, Hadamard's determinant inequality

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