Orthogonal Matchings

Dynamic matchings and quasidynamic fractional matchings. II

Consider a directed graph G in which every edge has an associated real-valued distance and a real-valued weight. The weight of an undirected circuit of G is the sum of the weights of the edges, whereas the distance of an undirected circuit is the sum of the distances of the forward edges of the circuit minus the sum of the distances of the backward edges. A trivial circuit is a two-edge circuit...

Dynamic matchings and quasidynamic fractional matchings. I

This paper presents and solves in polynomial time the dynamic matching problem, an integer programming problem which involves matchings in a time-expanded infinite network. The initial model is a finite directed graph G = (V, E) in which each edge has an associated real-valued weight and an integral distance. We wish to "match" vertices over an infinite horizon, and we permit vertex i in period...

Perfect Matchings in Edge-Transitive Graphs

We find recursive formulae for the number of perfect matchings in a graph G by splitting G into subgraphs H and Q. We use these formulas to count perfect matching of P hypercube Qn. We also apply our formulas to prove that the number of perfect matching in an edge-transitive graph is , where denotes the number of perfect matchings in G, is the graph constructed from by deleting edges with an en...

Coalitional matchings

In a coalitional two-sided matching problem agents on each side of the market may form coalitions such as student groups and research teams who – when matched – form universities. We assume that each researcher has preferences over the research teams he would like to work in and over the student groups he would like to teach to. Correspondingly, each student has preferences over the groups of s...

Popular Matchings