Graphs with no induced five-vertex path or antipath
| Autor: | Chudnovsky, Maria, Esperet, Louis, Lemoine, Laetitia, Maceli, Peter, Maffray, Frédéric, Penev, Irena |
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| Rok vydání: | 2014 |
| Předmět: | |
| Zdroj: | J. Graph Theory 84(3) (2017), 221-232 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1002/jgt.22022 |
| Popis: | We prove that a graph $G$ contains no induced $5$-vertex path and no induced complement of a $5$-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. Comment: 13 pages, the paper results from the merging of the two (unpublished) manuscripts 'Excluding four-edge paths and their complements', by M. Chudnovsky, P. Maceli and I. Penev arXiv:1302.0405 , and 'On $(P_5, \overline{P_5})$-free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) |
| Databáze: | arXiv |
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