Bounds for the chromatic index of signed multigraphs

Abstract

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