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arXiv · 2208.01001

Two New Characterizations of Path Graphs

Nicola Apollonio·Lorenzo Balzotti
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Abstract

Path graphs are intersection graphs of paths in a tree. We start from the characterization of path graphs by Monma and Wei [C.L.~Monma,~and~V.K.~Wei, Intersection Graphs of Paths in a Tree, J. Combin. Theory Ser. B, 41:2 (1986) 141--181] and we reduce it to some 2-colorings 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.

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Nicola Apollonio, Lorenzo Balzotti. 2022-08-01. Two New Characterizations of Path Graphs. https://arxiv.org/abs/2208.01001

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