{"paper":{"title":"Minimum Dominating Sets in Scale-Free Network Ensembles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","cs.SI"],"primary_cat":"physics.soc-ph","authors_text":"B.K. Szymanski, F. Molnar Jr., G. Korniss, S. Sreenivasan","submitted_at":"2013-02-11T16:06:32Z","abstract_excerpt":"We study the scaling behavior of the size of minimum dominating set (MDS) in scale-free networks, with respect to network size $N$ and power-law exponent $\\gamma$, while keeping the average degree fixed. We study ensembles generated by three different network construction methods, and we use a greedy algorithm to approximate the MDS. With a structural cutoff imposed on the maximal degree ($k_{\\max}=\\sqrt{N}$) we find linear scaling of the MDS size with respect to $N$ in all three network classes. Without any cutoff ($k_{\\max}=N-1$) two of the network classes display a transition at $\\gamma \\ap"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.2518","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"}