Chromatic Index, Treewidth and Maximum Degree

Henning Bruhn, Laura Gellert, Richard Lang


We conjecture that any graph $G$ with treewidth $k$ and maximum degree $\Delta(G)\geq k + \sqrt{k}$ satisfies $\chi'(G)=\Delta(G)$. In support of the conjecture we prove its fractional version. We also show that any graph $G$ with treewidth $k\geq 4$ and maximum degree $2k-1$ satisfies $\chi'(G)=\Delta(G)$, extending an old result of Vizing.


Graph theory; Edge colouring; Fractional edge colouring; Tree width

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