Year: 2026
Type: preprint
Abstract: We prove that every finite loopless signed multigraph $Σ=(G,σ)$ satisfies $χ'(Σ)\leqΔ(G)+μ(G)$, where $χ'(Σ)$ is its chromatic index, and $Δ(G)$ and $μ(G)$ are the maximum degree and maximum multiplicity of $G$, respectively. This bound is sharp, even when both positive and negative edges are present, and generalizes both Vizing's theorem for ordinary multigraphs and Behr's theorem for signed simple graphs.
Source: arXiv (Cornell University)
Authors: Lu, You, Zhao, Jingru, Zhang, Li
Institutions: Northwestern Polytechnical University, Yan'an University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Award: G6788329125
OpenAlex ID: W7214804048