Approximate proof labeling schemes were introduced by Censor-Hillel, Paz and Perry [3]. Roughly speaking, a graph property $\mathcal{P}$ 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 $\mathcal{P}$ or at least they are not far from being having the property $\mathcal{P}$. 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.

中文翻译：

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平面性可以通过恒定时间的近似证明标记方案来验证

Censor-Hillel、Paz 和 Perry [3] 介绍了近似证明标记方案。粗略地说，一个图属性$\mathcal{磷}$如果具有该属性的图的顶点可以在短时间内确信它们具有该属性，则可以通过恒定时间的近似证明标记方案来验证$\mathcal{磷}$或者至少他们离拥有房产不远了$\mathcal{磷}$. 本文的主要结果是，有界度平面图（以及外平面图、有界属图、无节可嵌入图等）可以在恒定时间内通过近似证明标记方案进行验证。