Two new characterizations of path graphs

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Nicola Apollonio, Lorenzo Balzotti

Published: 01 Jan 2023, Last Modified: 09 Feb 2025Discret. Math. 2023EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: 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.