{"paper":{"title":"The intersection graph of ideals of $\\mathbb{Z}_n$ is\\\\ weakly perfect","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"M.J. Nikmehr, R.Nikandish","submitted_at":"2013-05-27T18:29:12Z","abstract_excerpt":"A graph is called weakly perfect if its vertex chromatic number equals its clique number. Let $R$ be a ring and $I(R)^*$ be the set of all left proper non-trivial ideals of $R$. The intersection graph of ideals of $R$, denoted by $G(R)$, is a graph with the vertex set $I(R)^*$ and two distinct vertices $I$ and $J$ are adjacent if and only if $I\\cap J\\neq 0$. In this paper, it is shown that $G(\\mathbb{Z}_n)$, for every positive integer $n$, is a weakly perfect graph. Also, for some values of $n$, we give an explicit formula for the vertex chromatic number of $G(\\mathbb{Z}_n)$. Furthermore, it i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6287","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"}