{"paper":{"title":"On the reduced Euler characteristic of independence complexes of circulant graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Francesco Romeo, Giancarlo Rinaldo","submitted_at":"2017-06-02T21:58:59Z","abstract_excerpt":"Let $G$ be the circulant graph $C_n(S)$ with $S\\subseteq\\{ 1,\\ldots,\\left \\lfloor\\frac{n}{2}\\right \\rfloor\\}$. We study the reduced Euler characteristic $\\tilde{\\chi}$ of the independence complex $\\Delta (G)$ for $n=p^k$ with $p$ prime and for $n=2p^k$ with $p$ odd prime, proving that in both cases $\\tilde{\\chi}$ does not vanish. We also give an example of circulant graph whose independence complex has $\\tilde{\\chi}$ equals to $0$, giving a negative answer to R. Hoshino."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00863","kind":"arxiv","version":5},"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"}