eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2024-08-23
61:1
61:16
10.4230/LIPIcs.MFCS.2024.61
article
ℋ-Clique-Width and a Hereditary Analogue of Product Structure
Hliněný, Petr
1
https://orcid.org/0000-0003-2125-1514
Jedelský, Jan
1
https://orcid.org/0000-0001-9585-2553
Masaryk University, Brno, Czech Republic
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol306-mfcs2024/LIPIcs.MFCS.2024.61/LIPIcs.MFCS.2024.61.pdf
product structure
hereditary class
clique-width
twin-width