Matchings and paths in the cube

Authors

Béla Bollobás, Faculty of MathematicsFollow
Imre Leader, Faculty of MathematicsFollow

Abstract

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

Recommended Citation

Bollobás, B., & Leader, I. (1997). Matchings and paths in the cube. Discrete Applied Mathematics, 75 (1), 1-8. https://doi.org/10.1016/S0166-218X(96)00076-5