Graph Searches and Their End Vertices

Abstract

For a graph search algorithm, the end vertex problem is concerned with which vertices of a graph can be the last visited by this algorithm. We characterize all maximum cardinality searches on chordal graphs and derive from this characterization a polynomial-time algorithm for the end vertex problem of maximum cardinality searches on chordal graphs. It is complemented by a proof of NP-completeness of the same problem on weakly chordal graphs. We also show linear-time algorithms for deciding end vertices of breadth-first searches on interval graphs and end vertices of lexicographic depth-first searches on chordal graphs.