Pairwise Compatibility Graphs: A Survey

Abstract

A graph $G=(V,E)$ is a pairwise compatibility graph (PCG) if there exists an edge-weighted tree $T$ and two nonnegative real numbers $d_{min}$ and $d_{max}$ such that each leaf $u$ of $T$ is a node of $V$ and there is an edge $(u,v) \in E$ if and only if $d_{min} \leq d_T (u, v) \leq d_{max}$, where $d_T (u, v)$ is the sum of weights of the edges on the unique path from $u$ to $v$ in $T$. In this article, we survey the state of the art concerning this class of graphs and some of its subclasses.