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Discrete Mathematics & Theoretical Computer Science |
It was conjectured by Reed [reed98conjecture] that for any graph $G$, the graph's chromatic number $χ (G)$ is bounded above by $\lceil Δ (G) +1 + ω (G) / 2\rceil$ , where $Δ (G)$ and $ω (G)$ are the maximum degree and clique number of $G$, respectively. In this paper we prove that this bound holds if $G$ is the line graph of a multigraph. The proof yields a polynomial time algorithm that takes a line graph $G$ and produces a colouring that achieves our bound.
Source : ScholeXplorer
IsRelatedTo ARXIV 1703.01089 Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.1703.01089
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