伪多扇与棒棒糖
Pseudo-multifan and Lollipop
AI总结：
本文发展了边着色图中的“伪多扇”与“棒棒糖”概念，并证明它们是研究小核度图边着色问题的有力工具，为解决Hilton和Zhao的核猜想提供了新方法。
摘要：
最大度为$Δ$的简单图$G$若满足$|E(G)|>Δ\lfloor |V(G)|/2\rfloor$，则称其为过满的。$G$的核，记为$G_Δ$，是由$G$中度为$Δ$的顶点导出的子图。显然，若$G$过满，则$G$的边色数为$Δ+1$。反之，Hilton和Zhao于1996年猜想：若$G$是$Δ\ge 3$且$Δ(G_Δ)\le 2$的简单连通图，则$χ'(G)=Δ+1$意味着$G$过满或$G=P^*$，其中$P^*$由Petersen图删除一个顶点得到（核猜想）。本文旨在发展“伪多扇”与“棒棒糖”的概念，并研究它们在边着色图中的性质。这些概念被证明是研究具有小核度的图的边着色问题的有力工具。
英文摘要：
A simple graph $G$ with maximum degree $Δ$ is \emph{overfull} if $|E(G)|>Δ\lfloor |V(G)|/2\rfloor$. The \emph{core} of $G$, denoted $G_Δ$, is the subgraph of $G$ induced by its vertices of degree $Δ$. Clearly, the chromatic index of $G$ equals $Δ+1$ if $G$ is overfull. Conversely, Hilton and Zhao in 1996 conjectured that if $G$ is a simple connected graph with $Δ\ge 3$ and $Δ(G_Δ)\le 2$, then $χ'(G)=Δ+1$ implies that $G$ is overfull or $G=P^*$, where $P^*$ is obtained from the Petersen graph by deleting a vertex (Core Conjecture). The goal of this paper is to develop the concepts of ``pseudo-multifan'' and ``lollipop'' and study their properties in an edge colored graph. These concepts turn out to be powerful tools in edge coloring graphs with a small core degree.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
