13 papers · 1 filter
Bricks that every removable edge is solitary
Jinxin Xue, Jun Ge, Fuliang Lu +1
A brick is a 3-connected graph such that has a perfect matching for any two distinct vertices . An edge in a matching covered graph is removable if…
Near-bipartite bricks in which every b-invariant edge is a forcing edge
Yaxian Zhang, Fuliang Lu
A connected graph is matching covered if it has at least one edge and every edge lies in some perfect matching.Lovász proved that every matching covered graph G can be uniquely dec…
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.…
Tight cuts in matching covered graphs
Fuliang Lu, Fengming Dong
An edge cut C of a graph G is tight if |C \M| = 1 for every perfect matching M of G. Barrier-cuts and 2-separation cuts, also referred to as ELP-cuts, are two important types of ti…
Adjacent vertices of small degree in minimal matching covered graphs
Xiaoling He, Fuliang Lu, Heping Zhang
A connected graph with at least two vertices is matching covered if each of its edges lies in a perfect matching. A matching covered graph is minimal if the removal of any edge…
On minimal k-factor-critical planar graphs
Qiuli Li, Fuliang Lu, Heping Zhang
A graph of order is said to be \emph{-factor-critical} () if the removal of any vertices results in a graph with a perfect matching. A -factor-critical gr…