论文标题
1-tough $（K_2 \ cup KK_1）$的汉密尔顿周期的一些条件 - 免费图
Some conditions for hamiltonian cycles in 1-tough $(K_2 \cup kK_1)$-free graphs
论文作者
论文摘要
令$ k \ geq 2 $为整数。我们说图$ g $是$（k_2 \ cup kk_1）$ - 如果不包含$ k_2 \ cup kk_1 $作为诱导子图，则免费。最近，Shi和Shan猜想，每1美元和$ 2K $连接的$（k_2 \ cup kk_1）$ - 免费图形是哈密顿人。在本文中，我们通过证明陈述来解决这一猜想。每$ 1 $ -Tough和$ k $连接的$（K_2 \ cup kk_1）$ - 至少$ \ frac {3（k-1）} {2} $的免费图是汉密尔顿人或彼得森图。
Let $k \geq 2$ be an integer. We say that a graph $G$ is $(K_2 \cup kK_1)$-free if it does not contain $K_2 \cup kK_1$ as an induced subgraph. Recently, Shi and Shan conjectured that every $1$-tough and $2k$-connected $(K_2 \cup kK_1)$-free graph is hamiltonian. In this paper, we solve this conjecture by proving the statement; every $1$-tough and $k$-connected $(K_2 \cup kK_1)$-free graph with minimum degree at least $\frac{3(k-1)}{2}$ is hamiltonian or the Petersen graph.
