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Well-Quasi-Ordered Classes of Bounded Clique-Width

Authors Maël Dumas , Aliaume Lopez

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LIPIcs.LICS.2026.38.pdf
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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph theory
  • Theory of computation → Formal languages and automata theory
Keywords
  • well-quasi-ordering
  • clique-width
  • automata theory
  • monoids
  • factorization forests
  • gap embedding

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Abstract

We study classes of graphs with bounded clique-width that are well-quasi-ordered by the induced subgraph relation, in the presence of labels on the vertices. We prove that, given a finite presentation of a class of graphs, one can decide whether the class is labelled-well-quasi-ordered. This answers positively to two conjectures of Pouzet in the restricted case of bounded clique-width classes. Namely, we prove that being labelled-well-quasi-ordered by a set of size 2 or by a well-quasi-ordered infinite set are equivalent conditions, and that in such cases, one can freely assume that the graphs are equipped with a total ordering on their vertices. Finally, we provide a structural characterization of those classes as those that are of bounded clique-width and do not existentially transduce the class of all finite paths.

Cite As Get BibTex

Maël Dumas and Aliaume Lopez. Well-Quasi-Ordered Classes of Bounded Clique-Width. In 41st Annual Symposium on Logic in Computer Science (LICS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 380, pp. 38:1-38:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.LICS.2026.38

Author Details

Maël Dumas
  • University of Warsaw, Poland
Aliaume Lopez
  • INP Bordeaux, LaBRI, CNRS, France

Funding

  • Dumas, Maël: Maël Dumas was supported by the ERC project BUKA (n° 101126229) (during his employment in BUKA) and project BOBR (during his employment in BOBR) that received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 948057).

Acknowledgements

The authors would like to thank the Zygmunt Zaleski fundation for supporting the authors during the preparation of this work.

References

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