CC BY-NC-ND 4.0 UnportedJahnel, BenediktTóbiás, András2022-06-172022-06-172022https://oa.tib.eu/renate/handle/123456789/9064https://doi.org/10.34657/8102We consider undirected graphs that arise as deterministic functions of stationary point processes such that each point has degree bounded by two. For a large class of point processes and edge-drawing rules, we show that the arising graph has no infinite connected component, almost surely. In particular, this extends our previous result for signal-to-interference ratio graphs based on stabilizing Cox point processes and verifies the conjecture of Balister and Bollobás that the bidirectional k-nearest neighbor graph of a two-dimensional homogeneous Poisson point process does not percolate for k=2.enghttps://creativecommons.org/licenses/by-nc-nd/4.0/510bidirectional k-nearest neighbor graphcontinuum percolationdegree boundsdeletion-tolerancestationary point processesArticle