Brooks' theorem for 2-fold coloring

Authors

  • Jacob Anthony White University of Texas Rio Grande Valley

DOI:

https://doi.org/10.55016/ojs/cdm.v17i2.62707

Keywords:

Graph Coloring, Brook's Theorem, 2-fold coloring

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.

References

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Published

2022-12-29

Issue

Vol. 17 No. 2 (2022)

Section

Articles

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