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arXiv · 2206.11052

Bounds for the chromatic index of signed multigraphs

Eckhard Steffen·Isaak H. Wolf
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Abstract

The paper studies edge-coloring of signed multigraphs and extends classical Theorems of Shannon and König to signed multigraphs. We prove that the chromatic index of a signed multigraph $(G,σ_G)$ is at most $\lfloor \frac{3}{2} Δ(G) \rfloor$. Furthermore, the chromatic index of a balanced signed multigraph $(H,σ_H)$ is at most $Δ(H) + 1$ and the balanced signed multigraphs with chromatic index $Δ(H)$ are characterized.

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Eckhard Steffen, Isaak H. Wolf. 2023-05-25. Bounds for the chromatic index of signed multigraphs. https://doi.org/10.1016/j.dam.2023.05.008

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