Restricted extension of sparse partial edge colorings of hypercubes

C. J Casselgren; K. Markström; L. A. Pham

paper

Restricted extension of sparse partial edge colorings of hypercubes

arXiv:1711.01073

Abstract

We consider the following type of question: Given a partial proper $d$ -edge coloring of the $d$ -dimensional hypercube $Q_{d}$ , and lists of allowed colors for the non-colored edges of $Q_{d}$ ,can we extend the partial coloring to a proper $d$ -edge coloring using only colors from the lists? We prove that this question has a positive answer in the case when both the partial coloring and the color lists satisfy certain sparsity conditions.

Cited by in corpus (1)

On restricted colorings of $(d, s)$ -edge colorable graphs