Clique‐width: Harnessing the power of atoms-Reference-Cited by-同舟云学术

Clique‐width: Harnessing the power of atoms

Published:2023-07-10 Issue:4 Volume:104 Page:769-810
ISSN:0364-9024
Container-title:Journal of Graph Theory
language:en
Short-container-title:Journal of Graph Theory

Author:

Dabrowski Konrad K.¹^ORCID,Masařík Tomáš²³⁴^ORCID,Novotná Jana²³^ORCID,Paulusma Daniël⁵^ORCID,Rzążewski Paweł³⁶^ORCID

Affiliation:

1. School of Computing Newcastle University Newcastle upon Tyne UK

2. Faculty of Mathematics and Physics Charles University Prague Czech Republic

3. Institute of Informatics University of Warsaw Warsaw Poland

4. Department of Mathematics Simon Fraser University Burnaby Canada

5. Department of Computer Science Durham University Durham UK

6. Faculty of Mathematics and Information Science Warsaw University of Technology Warsaw Poland

Abstract

AbstractMany NP‐complete graph problems are polynomial‐time solvable on graph classes of bounded clique‐width. Several of these problems are polynomial‐time solvable on a hereditary graph class if they are so on the atoms (graphs with no clique cut‐set) of . Hence, we initiate a systematic study into boundedness of clique‐width of atoms of hereditary graph classes. A graph is ‐free if is not an induced subgraph of , and it is ‐free if it is both ‐free and ‐free. A class of ‐free graphs has bounded clique‐width if and only if its atoms have this property. This is no longer true for ‐free graphs, as evidenced by one known example. We prove the existence of another such pair and classify the boundedness of clique‐width on ‐free atoms for all but 18 cases.

Funder

Leverhulme Trust

Publisher

Wiley

Subject

Geometry and Topology,Discrete Mathematics and Combinatorics

Link

https://onlinelibrary.wiley.com/doi/pdf/10.1002/jgt.23000

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