dc.contributor.author | Chaplick, Steven | |
dc.contributor.author | Golovach, Petr | |
dc.contributor.author | Hartmann, Tim | |
dc.contributor.author | Knop, Dusan | |
dc.date.accessioned | 2021-05-19T13:04:07Z | |
dc.date.available | 2021-05-19T13:04:07Z | |
dc.date.created | 2021-01-04T13:01:15Z | |
dc.date.issued | 2020 | |
dc.Published | Leibniz International Proceedings in Informatics. 2020, 180 8:1-8:15. | |
dc.identifier.issn | 1868-8969 | |
dc.identifier.uri | https://hdl.handle.net/11250/2755716 | |
dc.description.abstract | We investigate the parameterized complexity of the recognition problem for the proper H-graphs. The H-graphs are the intersection graphs of connected subgraphs of a subdivision of a multigraph H, and the properness means that the containment relationship between the representations of the vertices is forbidden. The class of H-graphs was introduced as a natural (parameterized) generalization of interval and circular-arc graphs by Biró, Hujter, and Tuza in 1992, and the proper H-graphs were introduced by Chaplick et al. in WADS 2019 as a generalization of proper interval and circular-arc graphs. For these graph classes, H may be seen as a structural parameter reflecting the distance of a graph to a (proper) interval graph, and as such gained attention as a structural parameter in the design of efficient algorithms. We show the following results. - For a tree T with t nodes, it can be decided in 2^{𝒪(t² log t)} ⋅ n³ time, whether an n-vertex graph G is a proper T-graph. For yes-instances, our algorithm outputs a proper T-representation. This proves that the recognition problem for proper H-graphs, where H required to be a tree, is fixed-parameter tractable when parameterized by the size of T. Previously only NP-completeness was known. - Contrasting to the first result, we prove that if H is not constrained to be a tree, then the recognition problem becomes much harder. Namely, we show that there is a multigraph H with 4 vertices and 5 edges such that it is NP-complete to decide whether G is a proper H-graph. | en_US |
dc.language.iso | eng | en_US |
dc.publisher | Dagstuhl Publishing | en_US |
dc.rights | Navngivelse 4.0 Internasjonal | * |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/deed.no | * |
dc.title | Recognizing Proper Tree-Graphs | en_US |
dc.type | Journal article | en_US |
dc.type | Peer reviewed | en_US |
dc.description.version | publishedVersion | en_US |
dc.rights.holder | Copyright 2020 The Authors | en_US |
cristin.ispublished | true | |
cristin.fulltext | original | |
cristin.qualitycode | 1 | |
dc.identifier.doi | https://doi.org/10.4230/LIPIcs.IPEC.2020.8 | |
dc.identifier.cristin | 1864772 | |
dc.source.journal | Leibniz International Proceedings in Informatics | en_US |
dc.source.40 | 180 | |
dc.source.pagenumber | 8:1-8:15 | en_US |
dc.relation.project | Norges forskningsråd: 263317 | en_US |
dc.identifier.citation | Leibniz International Proceedings in Informatics. 2020, 180, 8:1-8:15 | en_US |
dc.source.volume | 180 | en_US |