Graphs with No Induced Five-Vertex Path or Antipath

Maria Chudnovsky; Louis Esperet; Laetitia Lemoine; Peter Maceli; Frédéric Maffray; Irena Penev

doi:10.1002/jgt.22022

Graphs with No Induced Five-Vertex Path or Antipath

Maria Chudnovsky, Louis Esperet, Laetitia Lemoine, Peter Maceli, Frédéric Maffray, Irena Penev

Department of Applied Mathematics and Computer Science

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Abstract

We prove that a graph G contains no induced five-vertex path and no induced complement of a five-vertex path if and only if G is obtained from 5-cycles and split graphs by repeatedly applying the following operations: substitution, split unification, and split unification in the complement, where split unification is a new class-preserving operation introduced here.

Original language	English
Journal	Journal of Graph Theory
Volume	84
Issue number	3
Pages (from-to)	221–232
ISSN	0364-9024
DOIs	https://doi.org/10.1002/jgt.22022
Publication status	Published - 2017

Bibliographical note

The accepted authors manuscript/post-print of this article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.

Keywords

Forbidden subgraph
P5
Decomposition

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10.1002/jgt.22022

2Accepted author manuscript, 285 KB

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AU - Lemoine, Laetitia

AU - Maceli, Peter

AU - Maffray, Frédéric

AU - Penev, Irena

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N2 - We prove that a graph G contains no induced five-vertex path and no induced complement of a five-vertex path if and only if G is obtained from 5-cycles and split graphs by repeatedly applying the following operations: substitution, split unification, and split unification in the complement, where split unification is a new class-preserving operation introduced here.

AB - We prove that a graph G contains no induced five-vertex path and no induced complement of a five-vertex path if and only if G is obtained from 5-cycles and split graphs by repeatedly applying the following operations: substitution, split unification, and split unification in the complement, where split unification is a new class-preserving operation introduced here.

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KW - P5

KW - Decomposition

U2 - 10.1002/jgt.22022

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Graphs with No Induced Five-Vertex Path or Antipath

Abstract

Bibliographical note

Keywords

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Cite this