Brooks' theorem for 2-fold coloring

Authors

Jacob A. White, The University of Texas Rio Grande Valley

Document Type

Article

Publication Date

12-29-2022

Abstract

The two-fold chromatic number of a graph is the minimum number of colors needed to ensure that there is a way to color the graph so that each vertex gets two distinct colors, and adjacent vertices have no colors in common. The Ore degree is the maximum sum of degrees of an edge in a graph. We prove that, for 2-connected graphs, the two-fold chromatic number is at most the Ore degree, unless G is a complete graph or an odd cycle.

Comments

Copyright (c) 2022 Contributions to Discrete Mathematics

Recommended Citation

White, Jacob Anthony. "Brooks' theorem for 2-fold coloring." Contributions to Discrete Mathematics 17.2 (2022): 67-76.

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.

Publication Title

Contributions to Discrete Mathematics