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In particular, this extends our previous result for signal\u2010to\u2010interference ratio graphs based on stabilizing Cox point processes and verifies the conjecture of Balister and Bollob\u00e1s that the bidirectional \u2010nearest neighbor graph of a two\u2010dimensional homogeneous Poisson point process does not percolate for .<\/jats:p>","DOI":"10.1002\/rsa.21084","type":"journal-article","created":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T07:29:14Z","timestamp":1648625354000},"page":"240-255","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Absence of percolation in graphs based on stationary point processes with degrees bounded by two"],"prefix":"10.1002","volume":"62","author":[{"given":"Benedikt","family":"Jahnel","sequence":"first","affiliation":[{"name":"Weierstrass Institute Berlin Berlin Germany"},{"name":"TU Braunschweig Braunschweig Germany"}]},{"given":"Andr\u00e1s","family":"T\u00f3bi\u00e1s","sequence":"additional","affiliation":[{"name":"TU Berlin Berlin Germany"}]}],"member":"311","published-online":{"date-parts":[[2022,3,30]]},"reference":[{"key":"e_1_2_6_2_1","first-page":"83","volume-title":"Recent results in designs and graphs: A tribute to Lucia Gionfriddo, Quaderni di Matematica","author":"Balister P.","year":"2013"},{"key":"e_1_2_6_3_1","doi-asserted-by":"publisher","DOI":"10.1214\/EJP.v18-2468"},{"issue":"2","key":"e_1_2_6_4_1","doi-asserted-by":"crossref","first-page":"1179","DOI":"10.1214\/19-AIHP998","article-title":"Absence of percolation for Poisson outdegree\u2010one graphs","volume":"56","author":"Coupier D.","year":"2020","journal-title":"Ann. 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A.KlattandG.Last On strongly rigid hyperfluctuating random measures 2020 arXiv:2008.10907."},{"key":"e_1_2_6_20_1","unstructured":"R.L\u00f6ffler Percolation phase transitions for the SIR model with random powers Master's thesis Technische Universit\u00e4t Berlin Institute of Mathematics 2019 arXiv:1908.07375."},{"key":"e_1_2_6_21_1","doi-asserted-by":"publisher","DOI":"10.1017\/9781316104477"},{"key":"e_1_2_6_22_1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511895357"},{"issue":"67","key":"e_1_2_6_23_1","first-page":"1","article-title":"Continuum percolation for Gibbs point processes","volume":"18","author":"Stucki K.","year":"2013","journal-title":"Electron. Commun. 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