{"paper":{"title":"The graphs with the max-Mader-flow-min-multiway-cut property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Guyslain Naves, Vincent Jost (LIX)","submitted_at":"2011-01-11T08:13:09Z","abstract_excerpt":"We are given a graph $G$, an independant set $\\mathcal{S} \\subset V(G)$ of \\emph{terminals}, and a function $w:V(G) \\to \\mathbb{N}$. We want to know if the maximum $w$-packing of vertex-disjoint paths with extremities in $\\mathcal{S}$ is equal to the minimum weight of a vertex-cut separating $\\mathcal{S}$. We call \\emph{Mader-Mengerian} the graphs with this property for each independant set $\\mathcal{S}$ and each weight function $w$. We give a characterization of these graphs in term of forbidden minors, as well as a recognition algorithm and a simple algorithm to find maximum packing of paths"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.2061","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":""},"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"}