{"paper":{"title":"Regularity of symbolic powers of edge ideals of Cameron-Walker graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"S. A. Seyed Fakhari","submitted_at":"2019-07-05T09:38:21Z","abstract_excerpt":"A Cameron-Walker graph is a graph for which the matching number and the induced matching number are the same. Assume that $G$ is a Cameron-Walker graph with edge ideal $I(G)$, and let $\\ind-match(G)$ be the induced matching number of $G$. It is shown that for every integer $s\\geq 1$, we have the equality ${\\rm reg}(I(G)^{(s)})=2s+\\ind-match(G)-1$, where $I(G)^{(s)}$ denotes the $s$-th symbolic power of $I(G)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.02743","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"}