论文标题
在哈密顿与迈西尔斯基的图形上
On Hamiltonian-Connected and Mycielski graphs
论文作者
论文摘要
如果在$ g $的任意两个顶点之间存在哈密顿式路径，则图表$ g $是与哈密顿的相关性。众所周知，如果$ g $是2个连接的，则图$ g^2 $是哈密顿式连接的。在本文中，我们证明，与4相关的每个自我平衡绘制图的平方是与4的平方。如果$ g $是$ k $ - 批判图，则我们证明Mycielski Graph $μ（g）$是$（k+1）$ - 关键图。 Jarnicki等[7]事实证明，对于每一个奇数订单的图表，$ g $的ycielski图$μ（g）$ g $ is hamiltonian连接。他们还提出了一个猜想，如果$ g $是与汉密尔顿连接的，而不是$ k_2 $，则$μ（g）$是汉密尔顿连接的。在本文中，我们还证明了这个猜想。
A graph $G$ is Hamiltonian-connected if there exists a Hamiltonian path between any two vertices of $G$. It is known that if $G$ is 2-connected then the graph $G^2$ is Hamiltonian-connected. In this paper we prove that the square of every self-complementary graph of order grater than 4 is Hamiltonian-connected. If $G$ is a $k$-critical graph, then we prove that the Mycielski graph $μ(G)$ is $(k+1)$-critical graph. Jarnicki et al.[7] proved that for every Hamiltonian graph of odd order, the Mycielski graph $μ(G)$ of $G$ is Hamiltonian-connected. They also pose a conjecture that if $G$ is Hamiltonian-connected and not $K_2$ then $μ(G)$ is Hamiltonian-connected. In this paper we also prove this conjecture.
