A Strong Edge-Coloring of Graphs with Maximum Degree 4 Using 22 Colors

Details A Strong Edge-Coloring of Graphs with Maximum Degree 4 Using 22 Colors A Strong Edge-Coloring of Graphs with Maximum Degree 4 Using 22 Colors

2006-01-25

arxiv.org/abs/math/0601623v1

Discrete Math. Vol. 306, no. 21, November 2006, pp. 2772-2778

Mathematics

Combinatorics

9 pages, 4 figures

Scientific paper

In 1985, Erd\H{o}s and Ne\'{s}etril 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.

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