Antipodal edge-colorings of hypercubes
Douglas B. West, Jenifer I. Wise · Discussiones Mathematicae Graph Theory · 2018
Two vertices of the k-dimensional hypercube Q k are antipodal if they differ in every coordinate. Edges uv and xy are antipodal if u is antipodal to x and v is antipodal to y. An antipodal edge-coloring of Q k is a 2edge-coloring such that antipodal edges always have different colors. Norine conjectured that for k 2, in every antipodal edge-coloring of Q k some two antipodal vertices are connected by a monochromatic path. Feder and Subi proved this for k 5. We prove it for k 6.