6 papers · 1 filter
On graphs with -matching and -matching edges
Yixuan Gao, Xiumei Wang, Jinfeng Liu
Let \(G\) be a graph admitting a perfect matching. An edge is called a {\it \(k\)-matching edge} if it belongs to exactly \(k\) perfect matchings, and a {\it \(k^{+}\)-matching edg…
The spectral radii and extremal graphs of two types of minimal graphs
Liwen Lian, Jinfeng Liu, Mengyuan Niu +1
A connected nontrivial graph is {\it matching covered} if every edge of is contained in some perfect matching of . A matching covered graph is {\it minimal} if …
Claw-free bricks that every -invariant edge is solitary
Yipei Zhang, Xiumei Wang
A graph is a brick if it is 3-connected and has a perfect matching for any two distinct vertices and of . Lucchesi and Murty proposed a problem concernin…
Solid bricks that every -invariant edge is solitary
Yipei Zhang, Xiumei Wang
A graph is a brick if it is 3-connected and has a perfect matching for any two distinct vertices and of . A brick is solid if for any two vertex disj…
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…
Claw-free minimal matching covered graphs
Yipei Zhang, Xiumei Wang, Jinjiang Yuan +2
A matching covered graph is minimal if for each edge of , is not matching covered. An edge of a matching covered graph is removable if is also matchi…