Matchings and paths in the cube


In this note we are concerned with the existence of matchings and families of disjoint paths between subsets of the n-dimensional discrete cube Qn. For example, we show that if A is a subset of Qn of size ∑ki=0(ni), where k < 1/2n, then there is a matching from A to its complement of size at least (nk). We also present a conjecture concerning the existence of directed paths, and prove some related results.

Publication Title

Discrete Applied Mathematics