Tree-width dichotomy
We prove that the tree-width of graphs in a hereditary class defined by a finite set F of forbidden induced subgraphs is bounded if and only if F includes a complete graph, a complete bipartite graph, a tripod (a forest in which every connected component has at most 3 leaves) and the line graph of a...
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| Published in | European journal of combinatorics Vol. 103; p. 103517 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.06.2022
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| ISSN | 0195-6698 1095-9971 |
| DOI | 10.1016/j.ejc.2022.103517 |
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| Abstract | We prove that the tree-width of graphs in a hereditary class defined by a finite set F of forbidden induced subgraphs is bounded if and only if F includes a complete graph, a complete bipartite graph, a tripod (a forest in which every connected component has at most 3 leaves) and the line graph of a tripod. |
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| AbstractList | We prove that the tree-width of graphs in a hereditary class defined by a finite set F of forbidden induced subgraphs is bounded if and only if F includes a complete graph, a complete bipartite graph, a tripod (a forest in which every connected component has at most 3 leaves) and the line graph of a tripod. |
| ArticleNumber | 103517 |
| Author | Lozin, Vadim Razgon, Igor |
| Author_xml | – sequence: 1 givenname: Vadim surname: Lozin fullname: Lozin, Vadim email: V.Lozin@warwick.ac.uk organization: Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK – sequence: 2 givenname: Igor surname: Razgon fullname: Razgon, Igor email: igor@dcs.bbk.ac.uk organization: Department of Computer Science and Information Systems, Birkbeck University of London, WC1E 7HX, UK |
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| Cites_doi | 10.1137/17M1145306 10.1016/S0166-218X(03)00387-1 10.4153/CJM-1959-003-9 10.1016/j.jctb.2004.08.001 10.1016/j.jctb.2019.04.004 10.1017/S0963548307008814 10.1016/0095-8956(86)90030-4 10.1016/S0304-3975(97)00228-4 10.1137/S0895480102419755 10.1007/s00493-004-0017-8 10.1016/j.jctb.2013.11.002 10.1016/S0166-218X(97)00031-0 |
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