{"paper":{"title":"Regularity of Powers of edge ideal of very well-covered graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Pooran Norouzi, Seyed Amin Seyed Fakhari, Siamak Yassemi","submitted_at":"2017-07-16T12:47:42Z","abstract_excerpt":"Let $k\\geq 3$ be an integer and $G$ be a very well-covered graph with ${\\rm odd-girth}(G)\\geq 2k+1$. Assume that $I(G)$ is the edge ideal of $G$. We show that for every integer $s$ with $1\\leq s\\leq k-2$, we have ${\\rm reg}(I(G)^s)=2s+\\nu(G)-1$, where $\\nu (G)$ is the induced matching number of $G$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.04874","kind":"arxiv","version":2},"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"}