Local certification of graph decompositions and applications to minor-free classes

Nicolas Bousquet (1) , Laurent Feuilloley (1) , Théo Pierron (1)

1 GOAL - Graphes, AlgOrithmes et AppLications

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 belongs to a given graph class. 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.

Mots clés: Local certification; proof-labeling schemes; locally checkable proofs; graph decompositions; minor-free graphs

Domaines: Informatique [cs]; Mathématiques [math]

Nicolas Bousquet, Laurent Feuilloley, Théo Pierron. Local certification of graph decompositions and applications to minor-free classes. 25th International Conference on Principles of Distributed Systems, OPODIS 2021, Dec 2021, Starsbourg, France. pp.22:1--22:17, ⟨10.4230/LIPIcs.OPODIS.2021.22⟩. ⟨hal-03772974⟩