{"paper":{"title":"Linear Residuals and Gallai-Simplicial Complexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Imran Anwar, Khurram Shabbir, Shaheen Nazir, Zunaira Kosar","submitted_at":"2016-12-12T05:13:03Z","abstract_excerpt":"In this paper, we give a new algebraic criterion for the {\\em shellability} of (non-pure) simplicial complex $\\Delta$ over $[n]$, shellable in the sense of Bj\\\"orner and Wachs \\cite{BW}. We show that the spanning simplicial complex of doubly uni-cyclic graph is non-pure shellable. Moreover, we introduce the concept of Gallai-simplicial complex $\\Delta_{\\Gamma}(G)$ of a finite simple graph $G$. We applied the obtained criterion to discuss the shellability of Gallai simplicial complexes associated to various classes of graphs.."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.03544","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"}