The algorithm of Micali and Vazirani [4] finds a maximum cardinality matching in time O( √ nm) if an efficient set-merging algorithm is used. The latter is provided by the incrementaltree set-merging algorithm of [2]. Details of this application to matching were omitted from [2] and are presented in this note.

Many markets have “unraveled” and experienced inefficient, early, dispersed transactions, and subsequently developed institutions to delay transaction timing. However, it has previously proved difficult to measure and identify the resulting efficiency gains. Prior to 1992, college football teams were matched for post-season play up to several weeks before the end of the regular season. Since 19...

We describe an abstract framework in which the notion of fundamental category can be defined. The structures matching this framework are categories endowed with some additional structure. Provided we have a suitable adjunction between two of them, the fundamental categories defined in both cases can be easily compared. Each of these structures has a “natural” functor to the category of d-spaces...

We consider the problem of finding a popular matching in the Capacitated House Allocation problem (CHA). An instance of CHA involves a set of agents and a set of houses. Each agent has a preference list in which a subset of houses are ranked in strict order, and each house may be matched to a number of agents that must not exceed its capacity. A matching M is popular if there is no other matchi...

LIFE uses matching on order-sorted feature structures for passing arguments to functions. As opposed to uni cation which amounts to normalizing a conjunction of constraints, solving a matching problem consists of deciding whether a constraint (guard) or its negation are entailed by the context. We give a complete and consistent set of rules for entailment and disentailment of order-sorted featu...

Let m be a positive integer and let G be a graph. A set M of matchings of G, all of which of size m, is called an [m]-covering of G if ⋃ M∈MM = E(G). G is called [m]-coverable if it has an [m]-covering. An [m]-covering M such that |M| is minimum is called an excessive [m]-factorization of G and the number of matchings it contains is a graph parameter called excessive [m]-index and denoted by χ[...

Given positive integers k ≥ 3 and l where k/2 ≤ l ≤ k − 1, we give a minimum ldegree condition that ensures a perfect matching in a k-uniform hypergraph. This condition is best possible and improves on work of Pikhurko who gave an asymptotically exact result, and extends work of Rödl, Ruciński and Szemerédi who determined the threshold for l = k − 1. Our approach makes use of the absorbing meth...

A graph G with at least 2m + 2 vertices is said to be distance d m-extendable if for any matching M of G with m edges in which the edges lie pair-wise distance at least d, there exists a perfect matching of G containing M . In this paper we prove that every 5-connected triangulation on the plane of even order is distance 3 9-extendable and distance 4 m-extendable for any m.

This paper considers marriage problems, roommate problems with nonempty core, and college admissions problems with responsive preferences. All stochastically stable matchings are shown to be contained in the set of matchings which are most robust to one-shot deviation.

Article history: Received 6 December 2006 Available online 26 July 2008