{"paper":{"title":"Feedback vertex number of Sierpi\\'{n}ski-type graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Baoyindureng Wu, Biao Zhao, LiLi Yuan","submitted_at":"2017-10-05T10:14:12Z","abstract_excerpt":"The feedback vertex number $\\tau(G)$ of a graph $G$ is the minimum number of vertices that can be deleted from $G$ such that the resultant graph does not contain a cycle. We show that $\\tau(S_p^n)=p^{n-1}(p-2)$ for the Sierpi\\'{n}ski graph $S_p^n$ with $p\\geq 2$ and $n\\geq 1$. The generalized Sierpi\\'{n}ski triangle graph $\\hat{S_p^n}$ is obtained by contracting all non-clique edges from the Sierpi\\'{n}ski graph $S_p^{n+1}$. We prove that $\\tau(\\hat{S}_3^n)=\\frac {3^n+1} 2=\\frac{|V(\\hat{S}_3^n)|} 3$, and give an upper bound for $\\tau(\\hat{S}_p^n)$ for the case when $p\\geq 4$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.01947","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"}