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.
@article{10_37236_9214,
author = {Scott Baldridge and Adam M. Lowrance and Ben McCarty},
title = {The 2-factor polynomial detects even perfect matchings},
journal = {The electronic journal of combinatorics},
year = {2020},
volume = {27},
number = {2},
doi = {10.37236/9214},
zbl = {1451.05120},
url = {http://geodesic.mathdoc.fr/articles/10.37236/9214/}
}
TY - JOUR
AU - Scott Baldridge
AU - Adam M. Lowrance
AU - Ben McCarty
TI - The 2-factor polynomial detects even perfect matchings
JO - The electronic journal of combinatorics
PY - 2020
VL - 27
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/9214/
DO - 10.37236/9214
ID - 10_37236_9214
ER -
%0 Journal Article
%A Scott Baldridge
%A Adam M. Lowrance
%A Ben McCarty
%T The 2-factor polynomial detects even perfect matchings
%J The electronic journal of combinatorics
%D 2020
%V 27
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/9214/
%R 10.37236/9214
%F 10_37236_9214
Scott Baldridge; Adam M. Lowrance; Ben McCarty. The 2-factor polynomial detects even perfect matchings. The electronic journal of combinatorics, Tome 27 (2020) no. 2. doi: 10.37236/9214
