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Author: Jahnel, Benedikt × DDC: 510 × Type: article × Subject: deletion-tolerance ×

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    Absence of percolation in graphs based on stationary point processes with degrees bounded by two
    (New York, NY [u.a.] : Wiley, 2022) Jahnel, Benedikt; Tóbiás, András
    We 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.