The matching preclusion set of a graph is a set of edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings. The matching preclusion number is the minimum cardinality over all matching preclusion sets. We show in this paper that, for any ≥  , the matching preclusion numbers of both -dimensional restricted HL-graph and recursive circulant  ...

The graphs considered here will be finite and will have no multiple edges. Let G be such a graph. A matching in G is a spanning subgraph whose components are nodes and edges only. We define a k-matching in G to be a matching with k edges. When the matching consists of edges only, it will be called a perfect matching. The number of perfect matchings in G will be denoted by y(G). The total number...

We give a TDI description for a class of polytopes which corresponds to a restricted 2-matching problem. The perfect matching polytope, triangle-free perfect 2-matching polytope and relaxations of the traveling salesman polytope are members of this class. For a class of restrictions G. Cornuéjols, D. Hartvigsen and W.R. Pulleyblank have shown that the unweighted problem is tractable; here we sh...

We show that deciding whether a given graph G of size m has a unique perfect matching as well as finding that matching, if it exists, can be done in time O(m) if G is either a cograph, or a split graph, or an interval graph, or claw-free. Furthermore, we provide a constructive characterization of the claw-free graphs with a unique perfect matching.

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 ...

Let α (G) denote the maximum size of an independent set of vertices and μ (G) be the cardinality of a maximum matching in a graph G. A matching saturating all the vertices is a perfect matching. If α (G) + μ (G) = |V (G)|, then G is called a König-Egerváry graph. A graph is unicyclic if it has a unique cycle. It is known that a maximum matching can be found in O(m •√n) time for a graph with n v...

In this paper we consider the computational complexity of deciding the existence of a perfect matching in certain classes of dense k-uniform hypergraphs. It has been known that the perfect matching problem for the classes of hypergraphs H with minimum ((k l)-wise) vertex degree o(H) at least clV(H)1 is NP-complete for c< -!;; and trivial for c 2': ~, leaving the status of the problem with c in ...

The idea of “forcing” has long been used in many research fields, such as colorings, orientations, geodetics and dominating sets in graph theory, as well as Latin squares, block designs and Steiner systems in combinatorics (see [1] and the references therein). Recently, the forcing on perfect matchings has been attracting more researchers attention. A forcing set of M is a subset of M contained...

In this paper it is shovm that every maximum matching in a 3-connectccl graph, other than ](4, contains at least one contractible edge. In the case of a. perfect ma.tching, those graphs in \vhich there exists a perfect matching containing precisely one contractible edge arc characterized.

A graph is called matching covered if for its every edge there is a maximum matching containing it. It is shown that minimal matching covered graphs contain a perfect matching.