论文标题
在常规的2个连接的2-Path Hamilton图中
On the regular 2-connected 2-path Hamiltonian graphs
论文作者
论文摘要
如果每一个不超过$ l $的长度路径都包含在汉密尔顿周期中，则图$ g $是$ l $ - Pather Hamiltonian。众所周知，如果每个边缘$ uv $ of $ g $，$ \ {u，v \} $，则最多3k-1 $ guntices是边缘 - hamiltonian，最多是$ 3K-1 $ vertices是边缘 - hamiltonian。因此，如果$ g \ setMinus \ {u，v \} $是为$ g $的每个边缘$ uv $连接的，则$ g $是1-path hamiltonian。令$ p = uvz $是2个连接的，$ k $的2个路径，最多是$ 2K $的顶点。在本文中，我们表明，如果连接了$ g \ setminus v（p）$，则有一个哈密顿周期，其中包含2-Path $ p $。因此，这项工作意味着有2个连接的，$ k $的图形为2-Path Hamiltonian的条件。一个示例表明，$ 2K $几乎是尖锐的，即，这个数字最多是$ 2K+1 $。
A graph $G$ is $l$-path Hamiltonian if every path of length not exceeding $l$ is contained in a Hamiltonian cycle. It is well known that a 2-connected, $k$-regular graph $G$ on at most $3k-1$ vertices is edge-Hamiltonian if for every edge $uv$ of $G$, $\{u,v\}$ is not a cut-set. Thus $G$ is 1-path Hamiltonian if $G\setminus \{u,v\}$ is connected for every edge $uv$ of $G$. Let $P=uvz$ be a 2-path of a 2-connected, $k$-regular graph $G$ on at most $2k$ vertices. In this paper, we show that there is a Hamiltonian cycle containing the 2-path $P$ if $G\setminus V(P)$ is connected. Therefore, the work implies a condition for a 2-connected, $k$-regular graph to be 2-path Hamiltonian. An example shows that the $2k$ is almost sharp, i.e., the number is at most $2k+1$.
