Vizing定理对于带符号多重图

中文摘要 AI 辅助

我们证明了每个有限无环带符号多重图Σ=(G,σ)满足χ'(Σ)≤Δ(G)+μ(G)，其中χ'(Σ)是其色指数，Δ(G)和μ(G)分别是G的最大度和最大重数。该界是紧的，即使同时存在正边和负边，并且推广了普通多重图的Vizing定理和带符号简单图的Behr定理。

英文摘要

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.

发表机构

• School of Mathematics and Statistics, Northwestern Polytechnical University（西北工业大学数学与统计学院）
• Yan’an University（延安大学）

机构由 AI 辅助整理，请以论文原文为准。