{"paper":{"title":"Sufficient conditions for a digraph to admit a $(1,\\leq\\ell)$-identifying code","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"B. Mart\\'inez-Barona, C. Balbuena, C. Dalf\\'o","submitted_at":"2019-02-13T14:21:26Z","abstract_excerpt":"A $(1,\\le \\ell)$-identifying code in a digraph $D$ is a subset $C$ of vertices of $D$ such that all distinct subsets of vertices of cardinality at most $\\ell$ have different closed in-neighborhoods within $C$. In this paper, we give some sufficient conditions for a digraph of minimum in-degree $\\delta^-\\ge 1$ to admit a $(1,\\le \\ell)$-identifying code for $\\ell=\\delta^-, \\delta^-+1$. As a corollary, we obtain the result by Laihonen that states that a graph of minimum degree $\\delta\\ge 2$ and girth at least 7 admits a $(1,\\le \\delta)$-identifying code. Moreover, we prove that every $1$-in-regul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.04913","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"}