{"paper":{"title":"The 3/5-conjecture for weakly $S(K_{1,3})$-free forests","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Simon Schmidt","submitted_at":"2015-07-10T12:33:42Z","abstract_excerpt":"The $3/5$-conjecture for the domination game states that the game domination numbers of an isolate-free graph $G$ on $n$ vertices are bounded as follows: $\\gamma_g(G)\\leq \\frac{3n}5 $ and $\\gamma_g'(G)\\leq \\frac{3n+2}5 $. Recent progress have been done on the subject and the conjecture is now proved for graphs with minimum degree at least $2$. One powerful tool, introduced by Bujt\\'as is the so-called greedy strategy for \\D. In particular, using this strategy, she has proved the conjecture for isolate-free forests without leafs at distance $4$. In this paper, we improve this strategy to extend"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02875","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"}