# matching

## Strong matchings and covers ★★★

Author(s): Aharoni

Let be a hypergraph. A *strongly maximal* matching is a matching so that for every matching . A *strongly minimal* cover is a (vertex) cover so that for every cover .

**Conjecture**If is a (possibly infinite) hypergraph in which all edges have size for some integer , then has a strongly maximal matching and a strongly minimal cover.

Keywords: cover; infinite graph; matching

## Matchings extend to Hamiltonian cycles in hypercubes ★★

Keywords: Hamiltonian cycle; hypercube; matching

## Ryser's conjecture ★★★

Author(s): Ryser

**Conjecture**Let be an -uniform -partite hypergraph. If is the maximum number of pairwise disjoint edges in , and is the size of the smallest set of vertices which meets every edge, then .

Keywords: hypergraph; matching; packing