Subgraphs of hypercubes and subdiagrams of boolean lattices

Optimal strong parity edge-coloring of complete graphs

“…Mitas and Reuter [20] later gave a much lengthier proof motivated by applying analogous methods to study subdiagrams of the subset lattice. They also characterized the graphs occurring as induced subgraphs of Q k as those having a k-edge-coloring satisfying properties (1) and ( 2) and ( 3), where property (3) essentially states that that if the parity vector of a walk W has weight 1, then the endpoints of W are adjacent.…”

“…Our work began by studying which graphs embed in the hypercube Q k , the graph with vertex set {0, 1} k in which vertices are adjacent when they differ in exactly one coordinate. Mitas and Reuter [20] motivated that question by observing that the hypercube is a common architecture for parallel computing. Coloring each edge with the position of the bit in which its endpoints differ yields two necessary conditions for the coloring inherited by a subgraph G:…”