有界树宽图的符号列表边着色
Signed list edge coloring in graphs of bounded treewidth
AI总结：
本文研究符号图的列表边着色，将经典列表边着色与符号边着色推广，证明树宽为3的符号图及树宽4且Δ≥10的符号图满足 Vizing 猜想的符号类似。
AI中文摘要：
Vizing 猜想：任意最大度为Δ的图的列表边色数不超过Δ+1，该猜想已在多类重要图中得证，其中 Lang 证明其对所有树宽为3的图成立。本文引入符号图的列表边着色（一种通用框架，推广了经典列表边着色与 Behr 提出的符号边着色），扩展 Lang 的结果，证明树宽为3的所有符号图满足 Vizing 猜想的符号类似，且树宽为4、最大度Δ≥10的符号图也满足该猜想。
英文摘要：
Vizing conjectured that the list edge chromatic number of any graph with maximum degree $Δ$ is at most $Δ+ 1$. This conjecture has been confirmed for several important classes of graphs, in particular, Lang proved that it holds for all graphs of treewidth $3$. In this paper, we introduce the list edge coloring of signed graphs, a framework that generalizes both classical list edge coloring and the signed edge coloring introduced by Behr. We extend Lang's result by proving the signed analogue of Vizing's conjecture for all signed graphs of treewidth $3$, as well as for signed graphs of treewidth $4$ with maximum degree $Δ\ge 10$.
