King图与Knight图中的蛇路径
Snake Paths in King and Knight Graphs
AI总结：
本文研究了King图与Knight图中的蛇路径，求出了$n \ imes n$ King图中蛇路径的最大长度并完整刻画了达到该长度的路径，同时估计了$m \ imes n$ Knight图中蛇路径或环的最大长度。
摘要：
图$G$中的蛇路径是$G$中同时作为$G$的导出子图的路径。对所有$n$，我们求出了$n \ imes n$ king图中蛇路径的最大长度，并完整描述了达到此最大长度的路径。奇偶情况表现迥异。我们还估计了所有$m$和$n$下$m \ imes n$ knight图中蛇路径或环的最大长度。
英文摘要：
A snake path in a graph $G$ is a path in $G$ which is also an induced subgraph of $G$. For all $n$, we find the greatest length of a snake path in the $n \times n$ king graph and we give a complete description of the paths which attain this greatest length. The even and odd cases behave very differently. We also estimate the greatest length of a snake path or cycle in the $m \times n$ knight graph, for all $m$ and $n$.
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。
