Planarity can be Verified by an Approximate Proof Labeling Scheme in Constant-Time

Elek, Gabor (2022) Planarity can be Verified by an Approximate Proof Labeling Scheme in Constant-Time. Journal of Combinatorial Theory, Series A, 191: 105643. ISSN 0097-3165

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Abstract

Approximate proof labeling schemes were introduced by Censor-Hillel, Paz and Perry. Roughly speaking, a graph property P can be verified by an approximate proof labeling scheme in constant-time if the vertices of a graph having the property can be convinced, in a short period of time not depending on the size of the graph, that they are having the property P or at least they are not far from being having the property P. The main result of this paper is that bounded-degree planar graphs (and also outer-planar graphs, bounded genus graphs, knotlessly embeddable graphs etc.) can be verified by an approximate proof labeling scheme in constant-time.