{"paper":{"title":"Very Well-Covered Graphs of Girth at least Four and Local Maximum Stable Set Greedoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Eugen Mandrescu, Vadim E. Levit","submitted_at":"2010-08-17T13:43:39Z","abstract_excerpt":"A \\textit{maximum stable set} in a graph $G$ is a stable set of maximum cardinality. $S$ is a \\textit{local maximum stable set} of $G$, and we write $S\\in\\Psi(G)$, if $S$ is a maximum stable set of the subgraph induced by $S\\cup N(S)$, where $N(S)$ is the neighborhood of $S$. Nemhauser and Trotter Jr. (1975), proved that any $S\\in\\Psi(G)$ is a subset of a maximum stable set of $G$. In (Levit & Mandrescu, 2002) we have shown that the family $\\Psi(T)$ of a forest $T$ forms a greedoid on its vertex set. The cases where $G$ is bipartite, triangle-free, well-covered, while $\\Psi(G)$ is a greedoid, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2897","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"}