Degrees and matchings

Perfect matchings (and Hamilton cycles) in hypergraphs with large degrees

We establish a new lower bound on the l-wise collective minimum degree which guarantees the existence of a perfect matching in a k-uniform hypergraph, where 1 ≤ l < k/2. For l = 1, this improves a long standing bound by Daykin and Häggkvist [4]. Our proof is a modification of the approach of Han, Person, and Schacht from [8]. In addition, we fill a gap left by the results solving a similar ques...

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...

Some perfect matchings and perfect half-integral matchings in NC

We show that for any class of bipartite graphs which is closed under edge deletion and where the number of perfect matchings can be counted in NC, there is a deterministic NC algorithm for finding a perfect matching. In particular, a perfect matching can be found in NC for planar bipartite graphs and K3,3-free bipartite graphs via this approach. A crucial ingredient is part of an interior-point...

I. Matchings and coverings