{"paper":{"title":"Perfect graphs for domination games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Csilla Bujt\\'as, Sandi Klav\\v{z}ar, Vesna Ir\\v{s}i\\v{c}","submitted_at":"2019-08-26T07:48:44Z","abstract_excerpt":"Let $\\gamma_g(G)$ and $\\gamma_{tg}(G)$ be the game domination number and the total game domination number of a graph $G$, respectively. Then $G$ is $\\gamma_g$-perfect (resp. $\\gamma_{tg}$-perfect), if every induced subgraph $F$ of $G$ satisfies $\\gamma_g(F)=\\gamma(F)$ (resp. $\\gamma_{tg}(F)=\\gamma_t(F)$). A recursive characterization of $\\gamma_g$-perfect graphs is derived. The characterization yields a polynomial recognition algorithm for $\\gamma_g$-perfect graphs. It is proved that every minimally $\\gamma_g$-imperfect graph has domination number $2$. All minimally $\\gamma_g$-imperfect triang"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.09513","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.09513/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}