{"paper":{"title":"Closing the Random Graph Gap in Tuza's Conjecture Through the Online Triangle Packing Process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrzej Dudek, Patrick Bennett, Ryan Cushman","submitted_at":"2020-07-08T23:50:43Z","abstract_excerpt":"A long-standing conjecture of Zsolt Tuza asserts that the triangle covering number $\\tau(G)$ is at most twice the triangle packing number $\\nu(G)$, where the triangle packing number $\\nu(G)$ is the maximum size of a set of edge-disjoint triangles in $G$ and the triangle covering number $\\tau(G)$ is the minimal size of a set of edges intersecting all triangles. In this paper, we prove that Tuza's conjecture holds in the Erd\\H{o}s-R\\'enyi random graph $G(n,m)$ for all range of $m$, closing the gap in what was previously known. (Recently, this result was also independently proved by Jeff Kahn and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.04478","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2007.04478/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}