Local Certification of Graph Decompositions and Applications to Minor-Free Classes

Authors Nicolas Bousquet , Laurent Feuilloley , Théo Pierron

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Author Details

Nicolas Bousquet
  • Univ. Lyon, Université Lyon 1, LIRIS UMR CNRS 5205, F-69621, Lyon, France
Laurent Feuilloley
  • Univ. Lyon, Université Lyon 1, LIRIS UMR CNRS 5205, F-69621, Lyon, France
Théo Pierron
  • Univ. Lyon, Université Lyon 1, LIRIS UMR CNRS 5205, F-69621, Lyon, France


The authors thank the reviewers for the their comments, and Jens M. Schmidt for pointing out a mistake a previous version.

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Nicolas Bousquet, Laurent Feuilloley, and Théo Pierron. Local Certification of Graph Decompositions and Applications to Minor-Free Classes. In 25th International Conference on Principles of Distributed Systems (OPODIS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 217, pp. 22:1-22:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


Local certification consists in assigning labels to the nodes of a network to certify that some given property is satisfied, in such a way that the labels can be checked locally. In the last few years, certification of graph classes received a considerable attention. The goal is to certify that a graph G belongs to a given graph class 𝒢. Such certifications with labels of size O(log n) (where n is the size of the network) exist for trees, planar graphs and graphs embedded on surfaces. Feuilloley et al. ask if this can be extended to any class of graphs defined by a finite set of forbidden minors. In this work, we develop new decomposition tools for graph certification, and apply them to show that for every small enough minor H, H-minor-free graphs can indeed be certified with labels of size O(log n). We also show matching lower bounds using a new proof technique.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Local certification
  • proof-labeling schemes
  • locally checkable proofs
  • graph decompositions
  • minor-free graphs


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