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Article Dans Une Revue Theoretical Computer Science Année : 2022

Local certification of graphs on surfaces

Louis Esperet
Benjamin Lévêque

Résumé

A proof labelling scheme for a graph class $\mathcal{C}$ is an assignment of certificates to the vertices of any graph in the class $\mathcal{C}$, such that upon reading its certificate and the certificate of its neighbors, every vertex from a graph $G\in \mathcal{C}$ accepts the instance, while if $G\not\in \mathcal{C}$, for every possible assignment of certificates, at least one vertex rejects the instance. It was proved recently that for any fixed surface $\Sigma$, the class of graphs embeddable in $\Sigma$ has a proof labelling scheme in which each vertex of an $n$-vertex graph receives a certificate of at most $O(\log n)$ bits. The proof is quite long and intricate and heavily relies on an earlier result for planar graphs. Here we give a very short proof for any surface. The main idea is to encode a rotation system locally, together with a spanning tree supporting the local computation of the genus via Euler's formula.
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Dates et versions

hal-03135544 , version 1 (22-07-2024)

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Louis Esperet, Benjamin Lévêque. Local certification of graphs on surfaces. Theoretical Computer Science, 2022, 909, pp.68-75. ⟨10.1016/j.tcs.2022.01.023⟩. ⟨hal-03135544⟩
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