Finding the set of all hinge vertices for strongly chordal graphs in linear time

Abstract

Let V( G) be the vertex set of a graph G = ( V,E), and let G — u be the subgraph induced by the vertex set V( G) - { u}. A vertex u ε V( G) is said to be a hinge vertex of G if and only if there exist two vertices x, y ε V( G-u) such that d G — u ( x,y) > d G ( x,y), where d G ( x, y) is the distance (the length of a shortest path) between x and y in G. In this paper, based on the breadth-first search technique, an O( n+ e) time algorithm is proposed for finding the set of all hinge vertices of a strongly chordal graph when a strong elimination ordering is given.