论文标题
非 - $ K $ -Choosable $ K $ -Chronic Graphs的不良列表分配，$ 2K+2 $ -vertices
Bad list assignments for non-$k$-choosable $k$-chromatic graphs with $2k+2$-vertices
论文作者
论文摘要
它由OHBA猜想，并由Noel，Reed和Wu证明，$ k $ -Chronic Graphs $ G $ with $ | v（g）| \ le 2k+1 $是色的。 $ | v（g）| $的上限很紧：如果$ k $均匀，则$ k_ {3 \ star（k/2+1），1 \ star（k/2-1）} $和$ k_ {4，2 \ star（k-1）} $是$ k $ k $ - 带有$ 2 k+2 $ 2 $ vertices的chrostic graphs，noce chrobable是$ 2 k+2 $ vertices。在[Arxiv：2201.02060]中证明，这些是唯一的非$ K $ -Choosable完整$ K $ - 分机图，$ 2K+2 $顶点。对于$ g = k_ {3 \ star（k/2+1），1 \ star（k/2-1）} $或$ k_ {4，2 \ star（k-1）} $，$ g $的不良列表分配是$ k $ list astist $ l-list tistment $ g $ g $ g $ g $ g $ g $ g $ g $ g $不可能$ l $ l $ colourable。 $ g = k_ {4，2 \ star（k-1）} $的坏列表分配在[离散数学244（2002），55-66]中进行了特征。在本文中，我们首先给出了更简单的证明，然后我们表征了$ g = k_ {3 \ star（k/2+1），1 \ star（k/2-1）} $的坏列表分配。使用这些结果，我们表征了所有非 - $ K $ -Choosable（不完整）$ K $ - 零件图，带有$ 2K+2 $顶点。
It was conjectured by Ohba, and proved by Noel, Reed and Wu that $k$-chromatic graphs $G$ with $|V(G)| \le 2k+1$ are chromatic-choosable. This upper bound on $|V(G)|$ is tight: if $k$ is even, then $K_{3 \star (k/2+1), 1 \star (k/2-1)}$ and $K_{4, 2 \star (k-1)}$ are $k$-chromatic graphs with $2 k+2$ vertices that are not chromatic-choosable. It was proved in [arXiv:2201.02060] that these are the only non-$k$-choosable complete $k$-partite graphs with $2k+2$ vertices. For $G =K_{3 \star (k/2+1), 1 \star (k/2-1)}$ or $K_{4, 2 \star (k-1)}$, a bad list assignment of $G$ is a $k$-list assignment $L$ of $G$ such that $G$ is not $L$-colourable. Bad list assignments for $G=K_{4, 2 \star (k-1)}$ were characterized in [Discrete Mathematics 244 (2002), 55-66]. In this paper, we first give a simpler proof of this result, and then we characterize bad list assignments for $G=K_{3 \star (k/2+1), 1 \star (k/2-1)}$. Using these results, we characterize all non-$k$-choosable (non-complete) $k$-partite graphs with $2k+2$ vertices.
