{"paper":{"title":"Spin-glass model for the C-dismantling problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.CO"],"primary_cat":"physics.soc-ph","authors_text":"Shao-Meng Qin","submitted_at":"2018-11-28T05:42:24Z","abstract_excerpt":"C-dismantling (CD) problem aims at finding the minimum vertex set D of a graph G(V,E) after removing which the remaining graph will break into connected components with the size not larger than C. In this paper, we introduce a spin-glass model with C+1 integer-value states into the CD problem and then study the properties of this spin-glass model by the belief-propagation (BP) equations under the replica-symmetry ansatz. We give the lower bound $\\rho_c$ of the relative size of D with finite C on regular random graphs and Erdos-Renyi random graphs. We find $\\rho_c$ will decrease gradually with "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.11394","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"}