Graphs with no induced five-vertex path or antipath
Combinatorics
2017-01-18 v2 Discrete Mathematics
Abstract
We prove that a graph contains no induced -vertex path and no induced complement of a -vertex path if and only if is obtained from -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.
Keywords
Cite
@article{arxiv.1410.0871,
title = {Graphs with no induced five-vertex path or antipath},
author = {Maria Chudnovsky and Louis Esperet and Laetitia Lemoine and Peter Maceli and Frédéric Maffray and Irena Penev},
journal= {arXiv preprint arXiv:1410.0871},
year = {2017}
}
Comments
13 pages, the paper results from the merging of the two (unpublished) manuscripts 'Excluding four-edge paths and their complements', by M. Chudnovsky, P. Maceli and I. Penev arXiv:1302.0405 , and 'On $(P_5, \overline{P_5})$-free graphs', by L. Esperet, L. Lemoine, and F. Maffray (2013)