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Well-Quasi-Ordering Eulerian Digraphs: Bounded Carving Width

Authors Dario Cavallaro , Ken-ichi Kawarabayashi , Stephan Kreutzer

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LIPIcs.ICALP.2026.51.pdf
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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph theory
Keywords
  • algorithmic graph theory
  • structural graph theory
  • digraphs
  • immersions
  • well-quasi ordering

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Abstract

We prove that every class of Eulerian directed graphs of bounded carving width (equivalently, of bounded degree and treewidth) is well-quasi-ordered by strong immersion. In fact, we prove a stronger result, namely that every class of Eulerian directed graphs of bounded carving width, where every vertex is additionally labelled from a well-quasi-order, fixes a linear order on its incident edges, and may impose further restrictions on how the immersion is allowed to route paths through it, is well-quasi-ordered by an adequate notion of strong immersion. To this extent, we develop a framework seemingly suited to prove well-quasi-ordering for classes of Eulerian directed graphs by (strong) immersion and present a first meta theorem in that direction. We complement our results by observing that the class of Eulerian directed graphs of unbounded degree is not well-quasi-ordered by strong immersion, even if we assume the treewidth of the class to be at most two. We conclude with a dichotomy result, proving for a very restricted class of Eulerian directed graphs of unbounded degree that it is not well-quasi-ordered by strong immersion, but it is well-quasi-ordered by weak immersion.

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Dario Cavallaro, Ken-ichi Kawarabayashi, and Stephan Kreutzer. Well-Quasi-Ordering Eulerian Digraphs: Bounded Carving Width. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 51:1-51:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ICALP.2026.51

Author Details

Dario Cavallaro
  • Technical University Berlin, Germany
Ken-ichi Kawarabayashi
  • National Institute of Informatics, Tokyo, Japan
  • The University of Tokyo, Japan
Stephan Kreutzer
  • Technical University Berlin, Germany

Funding

  • Kawarabayashi, Ken-ichi: Supported by JSPS Kakenhi 26K21777 and JP25K24465, and by JST ASPIRE JPMJAP2302.

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