关于线图补图的Hamilton性、traceability和toughness
On the Hamiltonicity, traceability and toughness of complements of line graphs
AI总结：
本文通过最长环方法证明了线图补图的Hamilton性特征化，并指出某些特定图如K_5的补图为彼得森图。
摘要：
一个图G的补线图co(G)是具有顶点集E(G)的图，其中两个顶点e和e'在co(G)中相邻当且仅当它们在G中不是相邻的边。一个图G是tough的，如果对于所有割集S，G-S的连通分量数目不超过|S|。吴和孟，以及刘独立地给出了类似的结果，即线图补图是Hamiltonian的特征化。在本文中，我们使用最长环方法给出了吴和孟以及刘的结果的另一种证明。我们实际上证明了他们结果的以下改写形式：一个tough的线图补图co(G)除非G是四个例子之一，其中一个是K_5，因为co(K_5)是彼得森图。还给出了tough线图和包含Hamiltonian路径的线图的特征化。
英文摘要：
A coline graph $\text{co}(G)$ of a graph $G$ is the graph with vertex set $E(G)$ for which two vertices $e$ and $e'$ of $\text{co}(G)$ are adjacent if and only if they are not adjacent as edges in $G$. A graph $G$ is tough if the number of connected components of $G-S$ is at most $|S|$ for all cut sets $S$. Wu and Meng, and Liu independently gave similar characterisations of coline graphs that are Hamiltonian. In this paper we give an alternate proof of Wu and Meng's and Liu's results using the longest cycle method. We in fact prove the following reformulation of their results. A tough coline graph $\text{co}(G)$ is Hamiltonian unless $G$ is one of four examples, one of which is $K_5$, since $\text{co}(K_5)$ is the Petersen graph. Characterisations of tough coline graphs and of coline graphs that contain a Hamiltonian path are also given.
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。
