{"paper":{"title":"A better bound on the largest induced forests in triangle-free planar graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hung Le","submitted_at":"2016-11-14T20:07:06Z","abstract_excerpt":"It is well-known that there exists a triangle-free planar graph of $n$ verticess such that the largest induced forest has size at most $\\frac{5n}{8}$. Salavatipour proved that there is a forest of size at least $\\frac{5n}{9.41}$ in any triangle-free planar graph of $n$ vertices. Dross, Montassier and Pinlou improved Salavatipour's bound to $\\frac{5n}{9.17}$. In this work, we further improve the bound to $\\frac{5n}{9}$. Our technique is inspired by the recent ideas from Lukot'ka, Maz{\\'a}k and Zhu."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04546","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"}