Markström, Klas , Casselgren, Carl Johan & Lan Anh Pham | 2020
Journal of Graph Theory
We consider the problem of extending partial edge colorings of hypercubes. In particular, we obtain an analogue of the positive solution to the famous Evans' conjecture on completing partial Latin squares by proving that every proper partial edge coloring of at most 𝑑−1 edges of the 𝑑 ‐dimensional hypercube 𝑄𝑑 can be extended to a proper 𝑑 ‐edge coloring of 𝑄𝑑 . Additionally, we characterize which partial edge colorings of 𝑄𝑑 with precisely 𝑑 precolored edges are extendable to proper 𝑑 ‐edge colorings of 𝑄𝑑.