The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. For many interconnection networks, the optimal sets are precisely those induced by a single vertex. Recently, the conditional matching preclusion number of a graph was introduced to look for obstruction sets beyond those inci...

The strong matching preclusion number of a graph is the minimum number of vertices and edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. This is an extension of the matching preclusion problem that was introduced by Park and Ihm. The burnt pancake graph is a more complex variant of the pancake graph. In this talk, we examine the properties ...

A graph is called perfect matching compact (briefly, PM -compact), if its perfect matching graph is complete. Matching-covered PM -compact bipartite graphs have been characterized. In this paper, we show that any PM -compact bipartite graph G with δ(G) ≥ 2 has an ear decomposition such that each graph in the decomposition sequence is also PM -compact, which implies that G is matching-covered.

Let F be a family of graphs. Two graphs G1 = (V1, E1), G2 = (V2, E2) are said to have the same F-structure if there is a bijection f : V1 → V2 such that a subset S induces a graph belonging to F in G1 if and only if its image f(S) induces a graph belonging to F in G2. We prove that graph H is perfect if and only if it has the {P3, P 3}-structure of some perfect graph G.

Kreweras’ conjecture [1] asserts that every perfect matching of the hypercube Qd can be extended to a Hamiltonian cycle. We [2] proved this conjecture but here we present a simplified proof. The matching graph M(G) of a graph G has a vertex set of all perfect matchings of G, with two vertices being adjacent whenever the union of the corresponding perfect matchings forms a Hamiltonian cycle. We ...