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2020•arXiv (Cornell University)Open access

A New Algorithm to Recognize Path Graphs and Directed Path Graphs.

Lorenzo Balzotti

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Abstract

A path graph is the intersection graph of paths in a tree. A directed path \ngraph is the intersection graph of paths in a directed tree. We present a new \nalgorithm to recognize path graphs and directed path graphs. It has the same \nworst-case time complexity as the faster recognition algorithms known so far \nbut it does not require complex data structures and it has an easy and \nintuitive implementation based on a new characterization of path graphs [N. \nApollonio and L. Balzotti, A New Characterization of Path Graphs, \narXiv:1911.09069, (2019).].

About this research paper

What this paper is about

A path graph is the intersection graph of paths in a tree. A directed path \ngraph is the intersection graph of paths in a directed tree. We present a new \nalgorithm to recognize path graphs and directed path graphs. It has the same \nworst-case time complexity as the faster recognition algorithms known so far \nbut it does not require complex data structures and it has an easy and \nintuitive implementation based on a new characterization of path graphs [N. \nApollonio and L. Balzotti, A New Characterization of Path Graphs, \narXiv:1911.09069, (2019).].

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Available abstract

A path graph is the intersection graph of paths in a tree. A directed path \ngraph is the intersection graph of paths in a directed tree. We present a new \nalgorithm to recognize path graphs and directed path graphs. It has the same \nworst-case time complexity as the faster recognition algorithms known so far \nbut it does not require complex data structures and it has an easy and \nintuitive implementation based on a new characterization of path graphs [N. \nApollonio and L. Balzotti, A New Characterization of Path Graphs, \narXiv:1911.09069, (2019).].

Key concepts: Longest path problem, Block graph, Path (computing), Computer science, Algorithm, Induced path, Chordal graph, Directed graph

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