Speaker：Fuliang Lu (Minnan Normal University)

Time：2024-7-25, 15:00

Location：Conference Room 686 at the 6th floor of Shuli Building at Haiyun Campus

Abstract:

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 nor G-f is. Removable edges and removable doubletons are called removable classes, which was introduced by Lovasz and Plummer in connection with ear decompositions of matching covered graphs.

A brick is a nonbipartite matching covered graph without nontrivial tight cuts. A brick G is wheel-like if G has a vertex h, such that every removable class of G has an edge incident with h. Lucchesi and Murty conjectured that every planar wheel-like brick is an odd wheel. In this talk, we will present some results about removable edges in a brick and a proof of this conjecture.