The concept of mutual-visibility in graphs has been recently introduced. If $X$ is a subset of vertices of a graph $G$, then vertices $u$ and $v$ are $X$-visible if there exists a shortest $u,v$-path $P$ such that $V(P)\cap X \subseteq \{u, v\}$. If every two vertices from $X$ are $X$-visible, then $X$ is a mutual-visibility set. The mutual-visibility number of $G$ is the cardinality of a largest mutual-visibility set of $G$. It is known that computing the mutual-visibility number of a graph is NP-complete, whereas it has been shown that there are exact formulas for special graph classes like paths, cycles, blocks, cographs, and grids. In this paper, we study the mutual-visibility in distance-hereditary graphs and show that the mutual-visibility number can be computed in linear time for this class.

翻译：互可视性的概念最近被引入图论中。若 $X$ 是图 $G$ 的顶点子集，则顶点 $u$ 与 $v$ 称为 $X$-可视的，当存在一条最短 $u,v$-路径 $P$ 使得 $V(P)\cap X \subseteq \{u, v\}$。若 $X$ 中任意两个顶点均为 $X$-可视的，则 $X$ 称为互可视集。图 $G$ 的互可视数定义为 $G$ 中最大互可视集的基数。已知计算图的互可视数是NP完全的，但已有研究表明路径、圈、块、余图及网格等特殊图类存在精确公式。本文研究了距离遗传图中的互可视性，并证明该图类的互可视数可在线性时间内计算。