{"paper":{"title":"Point determining digraphs, $\\{0,1\\}$-matrix partitions, and dualities in full homomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"C\\'esar Hern\\'andez-Cruz, Pavol Hell","submitted_at":"2013-08-01T23:50:29Z","abstract_excerpt":"We prove that every point-determining digraph $D$ contains a vertex $v$ such that $D-v$ is also point determining. We apply this result to show that for any $\\{0,1\\}$-matrix $M$, with $k$ diagonal zeros and $\\ell$ diagonal ones, the size of a minimal $M$-obstruction is at most $(k+1)(\\ell+1)$. This extends the results of Sumner, and of Feder and Hell, from undirected graphs and symmetric matrices to digraphs and general matrices."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0377","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"}