$\{K_{1,3},Γ_3\}$-free图中Hamilton-connectedness的一个闭包
A closure for Hamilton-connectedness in $\{K_{1,3},Γ_3\}$-free graphs
AI总结：
本文引入一种闭包技术，将$\{K_{1,3},Γ_3\}$-free图转化为多重图的线图并保持其Hamilton-connectedness，为后续证明$3$-连通图满足该性质及解决禁用子图对刻画的开放情形奠定基础。
摘要：
我们引入了$\{K_{1,3},Γ_3\}$-free图Hamilton-connectedness的闭包技术，其中$Γ_3$是用长度为$3$的路连接两个顶点不相交的三角形得到的图。该闭包将claw-free图转化为多重图的线图，同时保持其（非）Hamilton-connectedness。证明中最具技术性的部分是计算机辅助的。该闭包的主要应用在后续论文中给出，证明每个$3$-连通的$\{K_{1,3},Γ_3\}$-free图都是Hamilton-connected的，从而解决了蕴含Hamilton-connectedness的连通禁用子图对刻画中最后两个开放情形之一。
英文摘要：
We introduce a closure technique for Hamilton-connectedness of $\{K_{1,3},Γ_3\}$-free graphs, where $Γ_3$ is the graph obtained by joining two vertex-disjoint triangles with a path of length $3$. The closure turns a claw-free graph into a line graph of a multigraph while preserving its (non)-Hamilton-connectedness. The most technical parts of the proof are computer-assisted. The main application of the closure is given in a subsequent paper showing that every $3$-connected $\{K_{1,3},Γ_3\}$-free graph is Hamilton-connected, thus resolving one of the two last open cases in the characterization of pairs of connected forbidden subgraphs implying Hamilton-connectedness.
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。
