{"author":[{"first_name":"Thomas","full_name":"Richthammer, Thomas","id":"62054","last_name":"Richthammer"}],"user_id":"62054","date_created":"2026-02-18T12:17:42Z","_id":"64215","date_updated":"2026-02-18T12:23:17Z","language":[{"iso":"eng"}],"title":"Bunkbed conjecture for complete bipartite graphs and related classes of graphs","type":"preprint","status":"public","citation":{"apa":"Richthammer, T. (2022). <i>Bunkbed conjecture for complete bipartite graphs and related classes of graphs</i>.","mla":"Richthammer, Thomas. <i>Bunkbed Conjecture for Complete Bipartite Graphs and Related Classes of Graphs</i>. 2022.","bibtex":"@article{Richthammer_2022, title={Bunkbed conjecture for complete bipartite graphs and related classes of graphs}, author={Richthammer, Thomas}, year={2022} }","short":"T. Richthammer, (2022).","ama":"Richthammer T. Bunkbed conjecture for complete bipartite graphs and related classes of graphs. Published online 2022.","ieee":"T. Richthammer, “Bunkbed conjecture for complete bipartite graphs and related classes of graphs.” 2022.","chicago":"Richthammer, Thomas. “Bunkbed Conjecture for Complete Bipartite Graphs and Related Classes of Graphs,” 2022."},"abstract":[{"text":"Let G = (V, E) be a simple finite graph. The corresponding bunkbed graph G± consists of two copies G+ = (V +, E+), G− = (V −, E−) of G and additional edges connecting any two vertices v+ ∈ V+, v− ∈ V− that are the copies of a vertex v ∈ V . The bunkbed conjecture states that for independent bond percolation on G±, for all v, w ∈ V , it is more likely for\r\nv−, w− to be connected than for v−, w+ to be connected. While recently a counterexample for the bunkbed conjecture was found, it should still hold for many interesting classes of graphs, and here we give a proof for complete bipartite graphs, complete graphs minus the edges of a complete subgraph, and symmetric complete k-partite graphs.","lang":"eng"}],"year":"2022"}