{"paper":{"title":"Agent Arrangement Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.CO","authors_text":"Tadashi Sakuma, Tomoki Nakamigawa","submitted_at":"2012-12-11T05:46:18Z","abstract_excerpt":"An {\\em arrangement} of an ordered pair $(G_A, G_M)$ of graphs is defined as a function $f$ from $V(G_A)$ to $V(G_M)$ such that, for each vertex $c$ of $G_M$, the vertex-set $f^{-1}(c)$ of $G_A$ either is $\\emptyset$ (the case when $c \\not\\in f(V(G_A))$) or induces a connected subgraph of $G_A$ and that the family $\\{f^{-1}(y) : y \\in V(G_M), f^{-1}(y) \\neq \\emptyset\\}$ is a partition of $V(G_A)$. Let $f$ be an arrangement of $(G_A, G_M)$, let $pq$ be an edge of $G_M$ and let $U$ be a subset of $f^{-1}(p)$ such that each of the three graphs $G_A[U]$, $G_A[f^{-1}(p)\\setminus U]$ and $G_A[f^{-1}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.2306","kind":"arxiv","version":3},"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"}