涉及连通度的周长的一个下界
A Lower Bound for the Circumference Involving Connectivity
摘要：
设$G$是一个图，$C$是$G$中的最长圈，$\overline{p}$，$\overline{c}$分别是$G\backslash C$中的最长路和最长圈的长度.几乎所有的周长下限都基于一个标准的过程：在$G$中选择一个初始循环$C_0$，并试图通过$G\backslash C_0$的结构和与$\overline{p}$、$\overline{c}$和连接$κ$密切相关的$G\backslash C_0$和$G\backslash C_0$之间的连接来扩大它。实际上，在该过程的结果中获得的每个下界在某种程度上或与$κ$、$\overline{p}$、$\overline{c}$相关，但以$κ$、$\overline{p}$、$\overline{c}$的各种特定值的形式，并且主要问题是将这些不变量作为参数包含到这样的界中。本文给出了包含$δ$、$κ$和$\overline{c}$的周长的一个下界，并且这个下界随着$δ$、$κ$和$\overline{c}$的增加而增加.
英文摘要：
Let $G$ be a graph, $C$ a longest cycle in $G$ and $\overline{p}$, $\overline{c}$ the lengths of a longest path and a longest cycle in $G\backslash C$, respectively. Almost all lower bounds for the circumference base on a standard procedure: choose an initial cycle $C_0$ in $G$ and try to enlarge it via structures of $G\backslash C_0$ and connections between $C_0$ and $G\backslash C_0$ closely related to $\overline{p}$, $\overline{c}$ and connectivity $κ$. Actually, each lower bound obtained in result of this procedure, somehow or is related to $κ$, $\overline{p}$, $\overline{c}$ but in forms of various particular values of $κ$, $\overline{p}$, $\overline{c}$ and the major problem is to involve these invariants into such bounds as parameters. In this paper we present a lower bound for the circumference involving $δ$, $κ$ and $\overline{c}$ and increasing with $δ$, $κ$ and $\overline{c}$.
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