完美图类的加尾
Adding a Tail in Classes of Perfect Graphs
摘要：
考虑属于图类${\cal C}$的图$G$。我们感兴趣的是通过单个边缘$u w$将节点$w \not\in V(G)$连接到$G$，其中$u \in V(G)$ ;我们将这样的边缘称为\emph{tail}。由于在添加尾部之后由$G$产生的图（表示为$G+uw$）不需要属于类${\cal C}$，所以我们想要计算$G+w$的最小${\cal C}$ -完成，即，要添加到$G+uw$中的非边（不包括尾部$u w$）的最小数量，以便生成的图属于${\cal C}$。在本文中，我们研究这个问题的分裂，准阈值，阈值，和$P_4$ -稀疏图类，我们提出了线性时间算法，利用分裂图的结构和树表示的准阈值，阈值，和$P_4$ -稀疏图。
英文摘要：
Consider a graph $G$ which belongs to a graph class ${\cal C}$. We are interested in connecting a node $w \not\in V(G)$ to $G$ by a single edge $u w$ where $u \in V(G)$; we call such an edge a \emph{tail}. As the graph resulting from $G$ after the addition of the tail, denoted $G+uw$, need not belong to the class ${\cal C}$, we want to compute a minimum ${\cal C}$-completion of $G+w$, i.e., the minimum number of non-edges (excluding the tail $u w$) to be added to $G+uw$ so that the resulting graph belongs to ${\cal C}$. In this paper, we study this problem for the classes of split, quasi-threshold, threshold, and $P_4$-sparse graphs and we present linear-time algorithms by exploiting the structure of split graphs and the tree representation of quasi-threshold, threshold, and $P_4$-sparse graphs.
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。
