As far as we know, for most polynomially solvable network optimization problems, their inverse problems under l1 or l∞ norm have been studied, except the inverse maximum-weight matching problem in non-bipartite networks. In this paper we discuss the inverse problem of maximum-weight perfect matching in a non-bipartite network under l1 and l∞ norms. It has been proved that the inverse maximum-we...

Let R be a set of n red segments and B a set of n blue segments, we wish to find the minimum value d∗, such that there exists a perfect matching between R and B with bottleneck d∗, i.e., the maximum distance between a matched red-blue pair is d∗. We first solve the corresponding decision problem: Given R, B and a distance d > 0, find a maximum matching between R and B with bottleneck at most d....

For a graph G let L(G) and l(G) denote the size of the largest and smallest maximum matching of a graph obtained from G by removing a maximum matching of G. We show that L(G) ≤ 2l(G), and L(G) ≤ 3 2 l(G) provided that G contains a perfect matching. We also characterize the class of graphs for with L(G) = 2l(G). Our characterization implies the existence of a polynomial algorithm for testing the...

A graph G is induced matching extendable (shortly, IM-extendable), if every induced matching of G is included in a perfect matching of G. A graph G is claw-free, if G does not contain any induced subgraph isomorphic toK1,3. The kth power of a graphG, denoted byGk , is the graph with vertex set V (G) in which two vertices are adjacent if and only if the distance between them in G is at most k. I...

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 class of arrangement graphs was introduced as a common generalization of star graphs and alternating group g...

Given a positive integer n we find a graph G = (V,E) on |V | = n vertices with a minimum number of edges such that for any pair of non adjacent vertices x, y the graph G − x − y contains a (almost) perfect matching M . Intuitively the non edge xy and M form a (almost) perfect matching of G. Similarly we determine a graph G = (V,E) with a minimum number of edges such that for any matching M̄ of t...

Given a set of nodes and edges between them, what’s the maximum of number of disjoint edges? This problem is known as the graph matching problem, and its study has had an enormous impact on the develpoment of algorithms, combinatorics, optimization theory, and even complexity theory. Mathematicians have been interested in the matching problem since the 19th century, leading to celebrated theore...

In this paper, we show a necessary and sufficient condition which characterizes all factor critical graphs. Using this necessary and sufficient condition, we develop a linear time algorithm to determine whether a graph is factor critical if one of its maximum matchings is given. 1 Terminology and introduction All graphs considered in this paper are undirected, finite and simple. In general, we ...

With rapid changes in the business environment, organizations are increasingly looking at human resources as a unique asset that can provide sustained competitive advantage. As much as, people are viewed among the most important resources to firms, HR strategy would be central to achieve competitive advantages .Firms should view HR strategy as an important tool for integrating competencies insi...

The Hungarian method is an e cient algorithm for nding a minimal cost perfect matching in a weighted bipartite graph. This paper describes an e cient algorithm for nding all minimal cost perfect matchings. The computational time required to generate each additional perfect matching is O(n(n + m)); and it requires O(n+m) memory storage. This problem can be solved by algorithms for nding the Kth-...