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

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...

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Bibliographic Details
Published inDiscrete mathematics and theoretical computer science Vol. 27:2; no. Discrete Algorithms
Main Author Balzotti, Lorenzo
Format Journal Article
LanguageEnglish
Published Discrete Mathematics & Theoretical Computer Science 01.05.2025
Subjects
computer science - data structures and algorithms
f.2.2
g.2.2
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ISSN1365-8050
1462-7264
1365-8050
DOI10.46298/dmtcs.13355

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Summary: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. Comment: 13 pages, 3 figures
ISSN:1365-8050
1462-7264
1365-8050
DOI:10.46298/dmtcs.13355