Upper bounds for perfect matchings in pfaffian and planar graphs

Afshin Behmaram, Shmuel Friedland

Published 2012-10-25, updated 2012-12-31Version 2

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.