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(...

In this paper, we study the relationship between forbidden subgraphs and the existence of a matching. Let H be a set of connected graphs, each of which has three or more vertices. A graph G is said to beH-free if no graph inH is an induced subgraph of G. We completely characterize the setH such that every connected H-free graph of sufficiently large even order has a perfect matching in the foll...

Faudree, R.J., R.J. Gould and L.M. Lesniak, Neighborhood conditions and edge-disjoint perfect matchings, Discrete Mathematics 91 (1991) 33-43. A graph G satisfies the neighborhood condition ANC(G) 2 m if, for all pairs of vertices of G, the union of their neighborhoods has at least m vertices. For a fixed positive integer k, let G be a graph of even order n which satisfies the following conditi...

V := {ri}i=1 ∪ {ci}i=1 and E := {{ri, cj} | mi,j ≥ 1/n}. The main observation is that if G contains a perfect matching then there exists a desired permutation. To see that, let us assume that P = {e1, . . . , en} is a subset of the edges of G which form a perfect matching, with ei = {ri, cji}. Then setting π(i) := ji satisfies the desired properties: since P is a matching we have that π is a bi...

Matching extendability is significant in graph theory and its applications. The basic notion in this direction is n-extendability introduced by Plummer in 1980. Motivated by the different natures of bipartite matchings and non-bipartite matchings, this paper investigates bipartite-matching extendable (BM-extendable) graphs. A graph G is said to be BM-extendable if every matching M which is a pe...

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...

A near perfect matching is a matching covering all but one vertex in a graph. Let G be a connected graph and n ≤ (|V (G)|−2)/2 be a positive integer. If any n independent edges in G are contained in a near perfect matching, then G is said to be defect n-extendable. This paper presents two construction characterizations of defect n-extendable bipartite graphs and a necessary condition for minima...

In the fault diagnosis, the precision matching algorithm plays a very important role. The matching algorithms have been developed increasingly by considering main factors. We introduce several matching algorithms considered the combination of six essential factors. The each factor can affect the performance of the matching algorithm for fault diagnosis. The factors are applications of positive ...

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 generalized (n, k)-star graph was introduced to address scaling issues of the star graph, and it has many de...

For an arbitrary tree T, a T-matching in G is a set of vertex-disjoint subgraphs of G which are isomorphic to T. A T-matching which is a spanning subgraph of G is called a perfect T-matching. For any t-vertex tree T we find a threshold probability function jj = jj( n) for the existence of r edge-disjoint perfect T-matchings in a random graph G(n,p).