{"paper":{"title":"On the regularity of edge ideal 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":"2017-05-29T14:54:09Z","abstract_excerpt":"Let $G$ be a graph with $n$ vertices, $S=\\mathbb{K}[x_1,\\dots,x_n]$ be the polynomial ring in $n$ variables over a field $\\mathbb{K}$ and $I(G)$ denote the edge ideal of $G$. For every collection $\\mathcal{H}$ of connected graphs with $K_2\\in \\mathcal{H}$, we introduce the notions of $\\ind-match_{\\mathcal{H}}(G)$ and $\\min-match_{\\mathcal{H}}(G)$. It will be proved that the inequalities $\\ind-match_{\\{K_2, C_5\\}}(G)\\leq{\\rm reg}(S/I(G))\\leq\\min-match_{\\{K_2, C_5\\}}(G)$ are true. Moreover, we show that if $G$ is a Cohen--Macaulay graph with girth at least five, then ${\\rm reg}(S/I(G))=\\ind-matc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.10226","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"}