{"paper":{"title":"A remark on the independence number of sparse random Cayley sum graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Rajko Nenadov","submitted_at":"2025-03-03T22:34:13Z","abstract_excerpt":"The Cayley sum graph $\\Gamma_S$ of a set $S \\subseteq \\mathbb{Z}_n$ is defined on the vertex set $\\mathbb{Z}_n$, with an edge between distinct $x, y \\in \\mathbb{Z}_n$ if $x + y \\in S$. Campos, Dahia, and Marciano have recently shown that if $S$ is formed by taking each element in $\\mathbb{Z}_n$ independently with probability $p$, for $p > (\\log n)^{-1/80}$, then with high probability the largest independent set in $\\Gamma_S$ is of size $$\n  (2 + o(1)) \\log_{1/(1-p)}(n). $$ This extends a result of Green and Morris, who considered the case $p = 1/2$, and asymptotically matches the independence "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.02100","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/2503.02100/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"}