A Strong Edge-Coloring of Graphs with Maximum Degree 4 Using 22 Colors
Abstract
In 1985, Erdős and Neśetril conjectured that the strong edge-coloring number of a graph is bounded above by ${5/4}\Delta^2$ when $\Delta$ is even and ${1/4}(5\Delta^2-2\Delta+1)$ when $\Delta$ is odd. They gave a simple construction which requires this many colors. The conjecture has been verified for $\Delta\leq 3$. For $\Delta=4$, the conjectured bound is 20. Previously, the best known upper bound was 23 due to Horak. In this paper we give an algorithm that uses at most 22 colors.
- Publication:
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arXiv Mathematics e-prints
- Pub Date:
- January 2006
- DOI:
- 10.48550/arXiv.math/0601623
- arXiv:
- arXiv:math/0601623
- Bibcode:
- 2006math......1623C
- Keywords:
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- Mathematics - Combinatorics
- E-Print:
- 9 pages, 4 figures