{"paper":{"title":"On the decay of crossing numbers of sparse graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gelasio Salazar, Jesus Leanos, Jozsef Balogh","submitted_at":"2012-03-02T16:21:32Z","abstract_excerpt":"Richter and Thomassen proved that every graph has an edge $e$ such that the crossing number $\\ucr(G-e)$ of $G-e$ is at least $(2/5)\\ucr(G) - O(1)$. Fox and Cs. T\\'oth proved that dense graphs have large sets of edges (proportional in the total number of edges) whose removal leaves a graph with crossing number proportional to the crossing number of the original graph; this result was later strenghtened by \\v{C}ern\\'{y}, Kyn\\v{c}l and G. T\\'oth. These results make our understanding of the {decay} of crossing numbers in dense graphs essentially complete. In this paper we prove a similar result fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.0510","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"}