{"paper":{"title":"Large subgraphs without short cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Florent Foucaud, Guillem Perarnau, Michael Krivelevich","submitted_at":"2014-01-20T14:58:29Z","abstract_excerpt":"We study two extremal problems about subgraphs excluding a family $\\F$ of graphs. i) Among all graphs with $m$ edges, what is the smallest size $f(m,\\F)$ of a largest $\\F$--free subgraph? ii) Among all graphs with minimum degree $\\delta$ and maximum degree $\\Delta$, what is the smallest minimum degree $h(\\delta,\\Delta,\\F)$ of a spanning $\\F$--free subgraph with largest minimum degree? These questions are easy to answer for families not containing any bipartite graph. We study the case where $\\F$ is composed of all even cycles of length at most $2r$, $r\\geq 2$. In this case, we give bounds on $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.4928","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"}