Two New Characterizations of Path Graphs
Combinatorics
2022-08-02 v1 Discrete Mathematics
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.
Keywords
Cite
@article{arxiv.2208.01001,
title = {Two New Characterizations of Path Graphs},
author = {Nicola Apollonio and Lorenzo Balzotti},
journal= {arXiv preprint arXiv:2208.01001},
year = {2022}
}
Comments
18 pages, 6 figures