Two new characterizations of path graphs

Two new characterizations of path graphs

Path graphs are intersection graphs of paths in a tree. We start from the characterization of path graphs by Monma and Wei (1986) [14] and we reduce it to some 2-coloring subproblems, obtaining the first characterization that directly leads to a polynomial recognition algorithm. Then we introduce th...

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Veröffentlicht in:Discrete mathematics 2023-12, Vol.346 (12), p.113596, Article 113596
Hauptverfasser: Apollonio, Nicola, Balzotti, Lorenzo
Format: Artikel
Sprache:eng
Schlagworte:
Clique path tree
Minimal forbidden subgraphs
Path graphs
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Zusammenfassung:Path graphs are intersection graphs of paths in a tree. We start from the characterization of path graphs by Monma and Wei (1986) [14] and we reduce it to some 2-coloring subproblems, obtaining the first characterization that directly leads to a polynomial recognition algorithm. Then we introduce the collection of the attachedness graphs of a graph and we exhibit a list of minimal forbidden 2-edge colored subgraphs in each of the attachedness graph.
ISSN:0012-365X
DOI:10.1016/j.disc.2023.113596