# Strong edge-coloring of graphs with maximum degree 4 using 22 colors

```@article{Cranston2006StrongEO,
title={Strong edge-coloring of graphs with maximum degree 4 using 22 colors},
author={Daniel W. Cranston},
journal={Discret. Math.},
year={2006},
volume={306},
pages={2772-2778}
}```
In 1985, Erdos and Nesetril conjectured that the strong edge-coloring number of a graph is bounded above by 54@D^2 when @D is even and 14(5@D^2-2@D+1) when @D is odd. They gave a simple construction which requires this many colors. The conjecture has been verified for @D=<3. For @D=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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