Strong edge-coloring of graphs with maximum degree 4 using 22 colors
Copyright policy )Strong edge-coloring of graphs with maximum degree 4 using 22 colors
In 1985, Erdős and Neśetril conjectured that the strong edge-coloring number of a graph is bounded above by ${5/4}Δ^2$ when $Δ$ is even and ${1/4}(5Δ^2-2Δ+1)$ when $Δ$ is odd. They gave a simple construction which requires this many colors. The conjecture has been verified for $Δ\leq 3$. For $Δ=4$, 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.
9 pages, 4 figures
- University of Illinois System United States
- Office of Science United States
- University of Illinois at Urbana Champaign United States
- University of Illinois United States
- United States Department of Energy United States
Coloring of graphs and hypergraphs, FOS: Mathematics, edge-coloring, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Strong edge-coloring, Combinatorics (math.CO), Edge-coloring, strong edge-coloring, Theoretical Computer Science
Coloring of graphs and hypergraphs, FOS: Mathematics, edge-coloring, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Strong edge-coloring, Combinatorics (math.CO), Edge-coloring, strong edge-coloring, Theoretical Computer Science
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