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Generating Minimal Redundant and Maximal Irredundant Sets in Incidence Graphs

Authors Emanuel Castelo , Jérémie Chalopin , Oscar Defrain , Simon Vilmin

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LIPIcs.MFCS.2026.46.pdf
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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Enumeration algorithms
  • maximal irredundant sets
  • minimal redundant sets
  • incidence graphs

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Abstract

It has been proved by Boros and Makino that there is no output-polynomial-time algorithm enumerating the minimal redundant sets or the maximal irredundant sets of a hypergraph, unless P = NP. The same question was left open for graphs, with only a few tractable cases known to date. In this paper, we focus on graph classes that capture incidence relations such as bipartite, co-bipartite, and split graphs, motivated by their strong relation with hypergraphs. Concerning maximal irredundant sets, we show that the problem on co-bipartite graphs is as hard as in general graphs and tractable in split and strongly orderable graphs, the latter being a generalization of chordal bipartite graphs. As for minimal redundant sets enumeration, we first show that the problem is intractable in split and co-bipartite graphs, answering the aforementioned open question. Then, we show that it is tractable on (C₃,C₅,C₆,C₈)-free graphs, a class of graphs incomparable to strongly orderable graphs, and which also generalizes chordal bipartite graphs. Our positive results rely on the structural properties of these graph classes and thus cannot be easily extended to bipartite graphs, for which the question remains open for both problems.

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Emanuel Castelo, Jérémie Chalopin, Oscar Defrain, and Simon Vilmin. Generating Minimal Redundant and Maximal Irredundant Sets in Incidence Graphs. In 51st International Symposium on Mathematical Foundations of Computer Science (MFCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 386, pp. 46:1-46:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.MFCS.2026.46

Author Details

Emanuel Castelo
  • Aix-Marseille Université, CNRS, LIS, 13009 Marseille, France
Jérémie Chalopin
  • Aix-Marseille Université, CNRS, LIS, 13009 Marseille, France
Oscar Defrain
  • Aix-Marseille Université, CNRS, LIS, 13009 Marseille, France
Simon Vilmin
  • Aix-Marseille Université, CNRS, LIS, 13009 Marseille, France

Funding

  • Castelo, Emanuel: Supported by ANR project PARADUAL (ANR-24-CE48-0610-01).
  • Chalopin, Jérémie: Supported by ANR project MIMETIQUE (ANR-25-CE48-4089-01).
  • Defrain, Oscar: Supported by ANR project PARADUAL (ANR-24-CE48-0610-01).
  • Vilmin, Simon: Supported by ANR project PARADUAL (ANR-24-CE48-0610-01).

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