Excluding four-edge paths and their complements
Combinatorics
2015-12-08 v2 Discrete Mathematics
Abstract
We prove that a graph G contains no induced four-edge path and no induced complement of a four-edge path if and only if G is obtained from five-cycles and split graphs by repeatedly applying the following operations: substitution, split graph unification, and split graph unification in the complement ("split graph unification" is a new class-preserving operation that is introduced in this paper).
Keywords
Cite
@article{arxiv.1302.0405,
title = {Excluding four-edge paths and their complements},
author = {Maria Chudnovsky and Peter Maceli and Irena Penev},
journal= {arXiv preprint arXiv:1302.0405},
year = {2015}
}
Comments
28 pages, the paper arXiv:1410.0871 resulted from the merging of this manuscript together with 'On $(P_5, \overline{P_5})$-free graphs', by L. Esperet, L. Lemoine, and F. Maffray (2013)