论文标题
连接图的尖锐的矿石型条件，没有诱导恒星具有Hamiltonian路径
A sharp Ore-type condition for a connected graph with no induced star to have a Hamiltonian path
论文作者
论文摘要
我们说，如果$ g $有一个hamiltonian路径，则它的路径包含$ g $的所有顶点。对于图$ g $，令$σ_2（g）$表示两个$ g $的两个非附件顶点的最低度和; $σ_2（g）$的限制称为矿石型条件。给定一个整数$ t \ geq 5 $，我们证明，如果$ n $ vertices上的连接图形$ g $满足$σ_2（g）> {t-3 \ fover t-2} n $，则$ g $具有汉密尔顿路径或诱导的子差速度为iSmorphic is-graph isOmorphic to $ k_ $ k_ {1，t} $，t} $。此外，我们表征了所有$ n $ vertex图$ g $其中$σ_2（g）= {t-3 \ tot t-2} n $和$ g $既没有哈密顿路径，也不是诱导的子graph同构至$ k__ {1，t} $。这是Momège最近结果的类似物，他在$ t = 4 $的情况下调查了此案。
We say a graph $G$ has a Hamiltonian path if it has a path containing all vertices of $G$. For a graph $G$, let $σ_2(G)$ denote the minimum degree sum of two nonadjacent vertices of $G$; restrictions on $σ_2(G)$ are known as Ore-type conditions. Given an integer $t\geq 5$, we prove that if a connected graph $G$ on $n$ vertices satisfies $σ_2(G)>{t-3\over t-2}n$, then $G$ has either a Hamiltonian path or an induced subgraph isomorphic to $K_{1, t}$. Moreover, we characterize all $n$-vertex graphs $G$ where $σ_2(G)={t-3\over t-2}n$ and $G$ has neither a Hamiltonian path nor an induced subgraph isomorphic to $K_{1, t}$. This is an analogue of a recent result by Momège, who investigated the case when $t=4$.
