In the context of distributed certification, the recognition of graph classes has started to be intensively studied. For instance, different results related to the recognition of planar, bounded tree-width and $H$-minor free graphs have been recently obtained. The goal of the present work is to design compact certificates for the local recognition of relevant geometric intersection graph classes, namely interval, chordal, circular arc, trapezoid and permutation. More precisely, we give proof labeling schemes recognizing each of these classes with logarithmic-sized certificates. We also provide tight logarithmic lower bounds on the size of the certificates on the proof labeling schemes for the recognition of any of the aforementioned geometric intersection graph classes.

翻译：在分布式认证的背景下，图类的识别问题已开始受到深入研究。例如，关于平面图、有界树宽图和$H$-子式自由图识别的最新成果已相继涌现。本文旨在为若干重要几何交图类（即区间图、弦图、圆弧图、梯形图和置换图）的局部识别设计紧凑的证书。具体而言，我们提出了能够以对数规模证书识别这些图类的证明标记方案，并给出了关于上述任一几何交图类识别的证明标记方案中证书尺寸的紧对数下界。