Proving Norine's Conjecture holds for $n=7$ via SAT solvers

TL;DR

This paper verifies Norine's conjecture for the 7-dimensional cube graph using SAT solvers, extending prior proofs up to dimension 6 and confirming the conjecture's validity at this higher dimension.

Contribution

The paper introduces a SAT solver-based approach to prove Norine's conjecture for n=7, providing computational verification beyond previous theoretical results.

Findings

Norine's conjecture holds for n=7

SAT solvers effectively verify combinatorial conjectures

Extension of proven cases from n≤6 to n=7

Abstract

We say a red/blue edge-coloring of the $n$-dimensional cube graph, $Q_n$, is antipodal if all pairs of antipodal edges have different colors. Norine conjectured that in such a coloring there must exist a pair of antipodal vertices connected by a monochromatic path. Previous work has proven this conjecture for $n\le 6$. Using SAT solvers we verify that the conjecture holds for $n = 7$.