{"paper":{"title":"Dense graphs with a large triangle cover have a large triangle packing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Raphael Yuster","submitted_at":"2010-09-02T08:49:32Z","abstract_excerpt":"It is well known that a graph with $m$ edges can be made triangle-free by removing (slightly less than) $m/2$ edges. On the other hand, there are many classes of graphs which are hard to make triangle-free in the sense that it is necessary to remove roughly $m/2$ edges in order to eliminate all triangles. It is proved that dense graphs that are hard to make triangle-free, have a large packing of pairwise edge-disjoint triangles. In particular, they have more than $m(1/4+c\\beta^2)$ pairwise edge-disjoint triangles where $\\beta$ is the density of the graph and $c$ is an absolute constant. This i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0353","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"}