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.
Discrete Applied Mathematics
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