{"paper":{"title":"Improved bounds for the regularity of powers of edge ideals of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Seyed Amin Seyed Fakhari, Siamak Yassemi","submitted_at":"2018-05-30T12:37:57Z","abstract_excerpt":"Let $G$ be a graph with edge ideal $I(G)$. We recall the notions of $\\min-match_{\\{K_2, C_5\\}}(G)$ and $\\ind-match_{\\{K_2, C_5\\}}(G)$ from \\cite{sy}. We show that $${\\rm reg}(I(G)^s)\\leq 2s+\\min-match_{\\{K_2, C_5\\}}(G)-1,$$for all $s\\geq 1$, which implies that$${\\rm reg}(I(G)^s)\\leq 2s+\\min-match(G)-1.$$Moreover, we show that$${\\rm reg}(I(G)^s)\\geq 2s+\\ind-match_{\\{K_2, C_5\\}}(G)-2,$$and if $\\ind-match_{\\{K_2, C_5\\}}(G)$ is an odd integer, then$${\\rm reg}(I(G)^s)\\geq 2s+\\ind-match_{\\{K_2, C_5\\}}(G)-1.$$Furthermore, it is shown that$${\\rm reg}(I(G)^s)\\leq 2s+\\ord-match(G)-1,$$where $\\ord-match("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.12508","kind":"arxiv","version":3},"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"}