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ℋ-Clique-Width and a Hereditary Analogue of Product Structure

Authors Petr Hliněný , Jan Jedelský

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  • Mathematics of computing → Graph theory
Keywords
  • product structure
  • hereditary class
  • clique-width
  • twin-width

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Abstract

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.

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Petr Hliněný and Jan Jedelský. ℋ-Clique-Width and a Hereditary Analogue of Product Structure. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 61:1-61:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.MFCS.2024.61

Author Details

Petr Hliněný
  • Masaryk University, Brno, Czech Republic
Jan Jedelský
  • Masaryk University, Brno, Czech Republic

Acknowledgements

We acknowledge helpful discussions with Jakub Gajarský on the questions and problems posed in Section 5, and especially on the question of H-clique-width possibly being complement-closed.

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