{"paper":{"title":"Integral Biflow Maximization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guoli Ding, Mengxi Yang, Rongchuan Tao, Wenan Zang","submitted_at":"2024-07-25T07:24:13Z","abstract_excerpt":"Let $G=(V,E)$ be a graph with four distinguished vertices, two sources $s_1, s_2$ and two sinks $t_1,t_2$, let $c:\\, E \\rightarrow \\mathbb Z_+$ be a capacity function, and let ${\\cal P}$ be the set of all simple paths in $G$ from $s_1$ to $t_1$ or from $s_2$ to $t_2$. A biflow (or $2$-commodity flow) in $G$ is an assignment $f:\\, {\\cal P}\\rightarrow \\mathbb R_+$ such that $\\sum_{e \\in Q \\in {\\cal P}}\\, f(Q) \\le c(e)$ for all $e \\in E$, whose value is defined to be $\\sum_{Q \\in {\\cal P}}\\, f(Q)$. A bicut in $G$ is a subset $K$ of $E$ that contains at least one edge from each member of ${\\cal P}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.17821","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/2407.17821/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"}