5 papers · 1 filter
Wheel-like bricks and minimal matching covered graphs
Xiaoling He, Fuliang Lu, Jinxin Xue
A connected graph G with at least two vertices is matching covered if each of its edges lies in a perfect matching. We say that an edge e in a matching covered graph G is removable…
Cubic bricks that every b-invariant edge is forcing
Yaxian Zhang, Fuliang Lu, Heping Zhang
A connected graph G is matching covered if every edge lies in some perfect matching of G. Lovasz proved that every matching covered graph G can be uniquely decomposed into a list o…
Planar wheel-like bricks
Fuliang Lu, Jinxin Xue
An edge e in a matching covered graph G is removable if G-e is matching covered; a pair {e; f} of edges of G is a removable doubleton if G-e-f is matching covered, but neither G-e…
The number of perfect matchings in a brick
Fuliang Lu, Huali Pan
A 3-connected graph is a brick if the graph obtained from it by deleting any two distinct vertices has a perfect matching. The importance of bricks stems from the fact that they ar…
Removable edges in near-bipartite bricks
Yipei Zhang, Fuliang Lu, Xiumei Wang +1
An edge of a matching covered graph is removable if is also matching covered. The notion of removable edge arises in connection with ear decompositions of matching co…