Simpler and Unified Recognition Algorithm for Path Graphs and Directed Path Graphs

TL;DR

This paper introduces a unified, simple recognition algorithm for both path graphs and directed path graphs, extending recent characterizations and avoiding complex data structures.

Contribution

It presents the first unified recognition algorithm for path graphs and directed path graphs, simplifying existing methods and extending recent characterizations.

Findings

Algorithm is simple and easy to implement.

Unifies recognition procedures for both graph classes.

Extends recent characterizations to directed path graphs.

Abstract

A path graph is the intersection graph of paths in a tree. A directed path graph is the intersection graph of paths in a directed tree. Even if path graphs and directed path graphs are characterized very similarly, their recognition algorithms differ widely. We further unify these two graph classes by presenting the first recognition algorithm for both path graphs and directed path graphs. We deeply use a recent characterization of path graphs, and we extend it to directed path graphs. Our algorithm does not require complex data structures and has an easy and intuitive implementation, simplifying recognition algorithms for both graph classes.