Abstract The well-known -complete problem Matching Cut is to decide if a graph has matching that also an edge cut of the graph. We prove new complexity results for restricted H -free graphs, is, graphs do not contain some fixed as induced subgraph. two recently studied variants , on graphs. first variant requires must be extendable perfect second matching. In particular, we there exists small c...

In a bipartite graph G, a set S ⊆ V (G) is deficient if |N(S)| < |S|. A matching M (with vertex set U) is k-suitable if G − U has no deficient set of size less than k. Let fk(d) be the maximum r such that in the d-dimensional hypercube Qd every k-suitable matching having size at most r extends to a perfect matching. We generalize results of Limaye and Sarvate by proving that fk(d) = k(d− k) + (...

In this paper, we study matching integral graphs of small order. A graph is called matching integral if the zeros of its matching polynomial are all integers. Matching integral graphs were first studied by Akbari, Khalashi, etc. They characterized all traceable graphs which are matching integral. They studied matching integral regular graphs. Furthermore, it has been shown that there is no matc...

Let $G=(V,E)$ be a simple connected graph. A perfect matching (or Kekul'e structure in chemical literature) of $G$ is a set of disjoint edges which covers all vertices of $G$. The anti-forcing number of $G$ is the smallest number of edges such that the remaining graph obtained by deleting these edges has a unique perfect matching and is denoted by $af(G)$. In this paper we consider some specifi...

Let H = (V,E) be an r-uniform hypergraph and let F ⊂ 2 . A matching M of H is (α,F)perfect if for each F ∈ F , at least α|F | vertices of F are covered by M . Our main result is a theorem giving sufficient conditions for an r-uniform hypergraph to have a (1− ,F)-perfect matching. As a special case of our theorem we obtain the following result. Let K(n, r) denote the complete r-uniform hypergrap...

A bottleneck plane perfect matching of a set of n points in R is defined to be a perfect non-crossing matching that minimizes the length of the longest edge; the length of this longest edge is known as bottleneck. The problem of computing a bottleneck plane perfect matching has been proved to be NP-hard. We present an algorithm that computes a bottleneck plane matching of size at least n5 in O(...

A minimal blocker in a bipartite graph G is a minimal set of edges the removal of which leaves no perfect matching in G. We give a polynomial delay algorithm for finding all minimal blockers of a given bipartite graph. Equivalently, this gives a polynomial delay algorithm for listing the anti-vertices of the perfect matching polytope P (G) = {x ∈ R | Hx = e, x ≥ 0}, where H is the incidence mat...

In K(n, n) with edges colored either red or blue, we show that the problem of finding a solution matching, a perfect matching consisting of exactly r red edges, and (n− r) blue edges for specified 0 ≤ r ≤ n, is a nontrivial integer program. We present an alternative, logically simpler proof of a theorem in [3] which establishes necessary and sufficient conditions for the existance of a solution...

‎Unmixed bipartite graphs have been characterized by Ravindra and‎ ‎Villarreal independently‎. ‎Our aim in this paper is to‎ ‎characterize unmixed $r$-partite graphs under a certain condition‎, ‎which is a generalization of Villarreal's theorem on bipartite‎ ‎graphs‎. ‎Also, we give some examples and counterexamples in relevance to this subject‎.