3 papers
math.CO2026
Perfect matchings in planar 3-connected graphs: girth five and minimum degree five
Xinyu Dai
Let denote the number of perfect matchings of a graph . Goedgebeur et al. posted two questions about the perfect matchings of planar 3-connected graphs: does there exist…
math.CO2026
The number of perfect matchings in 3-connected planar graphs
Wuxian Chen, Xinyu Dai, Fuliang Lu
A graph is matchable if it admits a perfect matching. Recently, Goedgebeur et al. asked whether there exists a constant such that infinitely many matchable planar -connec…
math.CO2026
Bricks in which every vertex is incident with a forcing edge
Xinyu Dai, Fuliang Lu, Yaxian Zhang
A matching covered graph is a brick if it is 3-connected and bicritical. An edge of a matching covered graph G is a forcing edge if it lies in precisely one perfect matching of G.…