2026-07-25T06:45:40Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:20617 2024-08-23T05:50:29Z ddc:004 open_access

ℋ-Clique-Width and a Hereditary Analogue of Product Structure Hliněný, Petr Jedelský, Jan product structure hereditary class clique-width twin-width We introduce a novel generalization of the notion of clique-width which aims to bridge the gap between classical hereditary width measures and the recently introduced graph product structure theory. Bounding the new H-clique-width, in the special case of H being the class of paths, is equivalent to admitting a hereditary (i.e., induced) product structure of a path times a graph of bounded clique-width. Furthermore, every graph admitting the usual (non-induced) product structure of a path times a graph of bounded tree-width, has bounded H-clique-width and, as a consequence, it admits the usual product structure in an induced way. We prove further basic properties of H-clique-width in general. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Petr Hliněný and Jan Jedelský 2024 Is Part Of LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.MFCS.2024.61 urn:nbn:de:0030-drops-206176 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.61 eng https://creativecommons.org/licenses/by/4.0/legalcode