{"paper":{"title":"On dynamic monopolies of graphs with general thresholds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Manouchehr Zaker","submitted_at":"2011-03-06T10:20:44Z","abstract_excerpt":"Let $G$ be a graph and ${\\mathcal{\\tau}}: V(G)\\rightarrow \\Bbb{N}$ be an assignment of thresholds to the vertices of $G$. A subset of vertices $D$ is said to be dynamic monopoly (or simply dynamo) if the vertices of $G$ can be partitioned into subsets $D_0, D_1,..., D_k$ such that $D_0=D$ and for any $i=1,..., k-1$ each vertex $v$ in $D_{i+1}$ has at least $t(v)$ neighbors in $D_0\\cup ...\\cup D_i$. Dynamic monopolies are in fact modeling the irreversible spread of influence such as disease or belief in social networks. We denote the smallest size of any dynamic monopoly of $G$, with a given th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.1112","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"}