We describe optimal robust algorithms for finding a triangle and the unweighted girth in a unit disk graph, as well as finding a triangle in a transmission graph.In the robust setting, the input is not given as a set of sites in the plane, but rather as an abstract graph. The input may or may not be realizable as a unit disk graph or a transmission graph. If the graph is realizable, the algorithm is guaranteed to give the correct answer. If not, the algorithm will either give a correct answer or correctly state that the input is not of the required type.

翻译：我们描述了在单位圆盘图中寻找三角形及无权重围长，以及在传输图中寻找三角形的最优鲁棒算法。在鲁棒设置下，输入不是以平面上的站点集合形式给出，而是以抽象图的形式呈现。该输入可能或可能无法实现为单位圆盘图或传输图。若该图可实现，算法保证给出正确答案；若不可实现，算法将给出正确答案或正确指出输入不属于所需类型。