{"paper":{"title":"Some new sufficient conditions for $2p$-Hamilton-biconnectedness of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ming-Zhu Chen, Xiao-Dong Zhang","submitted_at":"2017-08-01T07:54:09Z","abstract_excerpt":"A balanced bipartite graph $G$ is said to be $2p$-Hamilton-biconnected if for any balanced subset $W$ of size $2p$ of $V(G)$, the subgraph induced by $V(G)\\backslash W$ is Hamilton-biconnected. In this paper, we prove that \"Let $p\\geq0$ and $G$ be a balanced bipartite graph of order $2n$ with minimum degree $\\delta(G)\\geq k$, where $n\\geq 2k-p+2$ and $k\\geq p$. If the number of edges $ e(G)>n(n-k+p-1)+(k+2)(k-p+1), $ then $G$ is $2p$-Hamilton-biconnected except some exceptions.\" Furthermore, this result is used to present two new spectral conditions for a graph to $2p$-Hamilton-biconnected. Mo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00196","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"}