[2208.01001] Two New Characterizations of Path Graphs
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Mathematics > Combinatorics

arXiv:2208.01001 (math)
[Submitted on 1 Aug 2022]

Title:Two New Characterizations of Path Graphs

Authors: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.
Comments: 18 pages, 6 figures
Subjects: Combinatorics (math.CO); Discrete Mathematics (cs.DM)
Cite as: arXiv:2208.01001 [math.CO]
  (or arXiv:2208.01001v1 [math.CO] for this version)
  https://doi.org/10.48550/arXiv.2208.01001

Submission history

From: Lorenzo Balzotti [view email]
[v1] Mon, 1 Aug 2022 17:16:27 UTC (1,203 KB)
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