{"paper":{"title":"Maximizing the Number of Spanning Trees in a Connected Graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.DS","authors_text":"Huan Li, Stacy Patterson, Yuhao Yi, Zhongzhi Zhang","submitted_at":"2018-04-09T01:20:38Z","abstract_excerpt":"We study the problem of maximizing the number of spanning trees in a connected graph by adding at most $k$ edges from a given candidate edge set. We give both algorithmic and hardness results for this problem:\n  - We give a greedy algorithm that, using submodularity, obtains an approximation ratio of $(1 - 1/e - \\epsilon)$ in the exponent of the number of spanning trees for any $\\epsilon > 0$ in time $\\tilde{O}(m \\epsilon^{-1} + (n + q) \\epsilon^{-3})$, where $m$ and $q$ is the number of edges in the original graph and the candidate edge set, respectively. Our running time is optimal with resp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.02785","kind":"arxiv","version":2},"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"}