Upper bounds for perfect matchings in pfaffian and planar graphs
Afshin Behmaram, Shmuel Friedland
TL;DR
This paper establishes improved upper bounds for weighted perfect matchings in pfaffian and planar graphs, demonstrating their sharpness in certain regular graphs and applying the results to fullerene structures.
Contribution
It introduces tighter upper bounds for perfect matchings in pfaffian graphs, surpassing Bregman's bounds, and shows their sharpness in specific regular cases, with applications to fullerene graphs.
Findings
New upper bounds are better than Bregman's bounds.
Some bounds are sharp for 3 and 4-regular pfaffian graphs.
Applications to fullerene graphs demonstrate practical relevance.
Abstract
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.