2026/07/19 by Wuxian Chen, Xinyu Dai, Fuliang Lu
#math.CO
A graph is matchable if it admits a perfect matching. Recently, Goedgebeur et al. asked whether there exists a constant c<12 such that infinitely many matchable planar 3-connected graphs, each with exactly c perfect matchings. We prove that every matchable planar 3-connected graphs on at least 40 vertices has at least 12 perfect matchings, and this lower bound is sharp. This answers the question negatively.