{"paper":{"title":"A Note on Bipartite Subgraphs and Triangle-independent Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Honghai Xu","submitted_at":"2015-12-19T07:45:53Z","abstract_excerpt":"Let $\\alpha_{1} (G)$ denote the maximum size of an edge set that contains at most one edge from each triangle of $G$. Let $\\tau_{B} (G)$ denote the minimum size of an edge set whose deletion makes $G$ bipartite. It was conjectured by Lehel and independently by Puleo that $\\alpha_{1} (G) + \\tau_{B} (G) \\le n^2/4$ for every $n$-vertex graph $G$. Puleo showed that $\\alpha_{1} (G) + \\tau_{B} (G) \\le 5n^2/16$ for every $n$-vertex graph $G$. In this note, we improve the bound by showing that $\\alpha_{1} (G) + \\tau_{B} (G) \\le 4403n^2/15000$ for every $n$-vertex graph $G$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.06202","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"}