Chromatic index, treewidth and maximum degree
Copyright policy )Chromatic index, treewidth and maximum degree
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.
- University of Ulm Germany
- University of Birmingham United Kingdom
- University of Chile Chile
graph theory, G.2.2, Fractional graph theory, fuzzy graph theory, tree width, edge colouring, 05C15, 05C72, 05C75, Coloring of graphs and hypergraphs, FOS: Mathematics, Mathematics - Combinatorics, fractional edge colouring, Structural characterization of families of graphs, Combinatorics (math.CO)
graph theory, G.2.2, Fractional graph theory, fuzzy graph theory, tree width, edge colouring, 05C15, 05C72, 05C75, Coloring of graphs and hypergraphs, FOS: Mathematics, Mathematics - Combinatorics, fractional edge colouring, Structural characterization of families of graphs, Combinatorics (math.CO)
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