The 2-factor polynomial detects even perfect matchings
In this paper, we prove that the 2-factor polynomial, an invariant of a planar trivalent graph with a perfect matching, counts the number of 2-factors that contain the perfect matching as a subgraph. Consequently, we show that the polynomial detects even perfect matchings.
Electronic Journal of Combinatorics
Baldridge, S., Lowrance, A., & McCarty, B. (2020). The 2-factor polynomial detects even perfect matchings. Electronic Journal of Combinatorics, 27 (2), 1-16. https://doi.org/10.37236/9214