{"paper":{"title":"Packing odd $T$-joins with at most two terminals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ahmad Abdi, Bertrand Guenin","submitted_at":"2014-10-27T20:40:43Z","abstract_excerpt":"Take a graph $G$, an edge subset $\\Sigma\\subseteq E(G)$, and a set of terminals $T\\subseteq V(G)$ where $|T|$ is even. The triple $(G,\\Sigma,T)$ is called a signed graft. A $T$-join is odd if it contains an odd number of edges from $\\Sigma$. Let $\\nu$ be the maximum number of edge-disjoint odd $T$-joins. A signature is a set of the form $\\Sigma\\triangle \\delta(U)$ where $U\\subseteq V(G)$ and $|U\\cap T)$ is even. Let $\\tau$ be the minimum cardinality a $T$-cut or a signature can achieve. Then $\\nu\\leq \\tau$ and we say that $(G,\\Sigma,T)$ packs if equality holds here.\n  We prove that $(G,\\Sigma,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7423","kind":"arxiv","version":2},"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"}