{"paper":{"title":"Maximum flow and self-avoiding walk on bunkbed graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Pengfei Tang","submitted_at":"2025-02-10T08:16:11Z","abstract_excerpt":"We consider two combinatorial models on bunkbed graphs: maximum flow and self-avoiding walks. A bunkbed graph is defined as the Cartesian product $G\\times K_2$, where $G$ is a finite graph and $K_2$ is the complete graph on two vertices, labelled $0$ and $1$. For the maximum flow problem, we show that if the bunkbed graph $G\\times K_2$ has non-negative, reflection-symmetric edge capacities, then for any $u, v\\in V(G)$, the maximum flow strength from $(u,0)$ to $(v,0)$ in $G\\times K_2$ is at least as large as that from $(u,0)$ to $(v,1)$.\n  For the self-avoiding walk model on a bunkbed graph $G"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.06237","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.06237/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}