{"paper":{"title":"Cycle Domination, Independence and Irredundance in graphs","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Amy Grady, Drew J. Lipman, Fiona Knoll, Renu Laskar","submitted_at":"2015-05-09T13:22:07Z","abstract_excerpt":"A set $S$ of vertices in a graph $G = (V, E)$ is called {\\em cycle independent} if the induced subgraph $\\langle S\\rangle$ is acyclic, and called {\\em odd-cycle indepdendet} if $\\langle S\\rangle$ is bipartite. A set $S$ is {\\em cycle dominating} (resp. {\\em odd-cycle dominating}) if for every vertex $u \\in V \\setminus S$ there exists a vertex $v \\in S$ such that $u$ and $v$ are contained in a (resp. odd cycle) cycle in $\\langle S \\setminus \\{u\\}\\rangle$. A set $S$ is {\\em cycle irredundant} (resp. odd-cycle irredundant) if for every vertex $v \\in S$ there exists a vertex $u \\in V \\setminus S$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02268","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"}