{"paper":{"title":"Dynamic monopolies in directed graphs: the spread of unilateral influence in social networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Hossein Soltani, Kaveh Khoshkhah, Manouchehr Zaker","submitted_at":"2012-12-15T13:22:25Z","abstract_excerpt":"Let $G$ be a directed graph such that the in-degree of any vertex $G$ is at least one. Let also ${\\mathcal{\\tau}}: V(G)\\rightarrow \\Bbb{N}$ be an assignment of thresholds to the vertices of $G$. A subset $M$ of vertices of $G$ is called a dynamic monopoly for $(G,\\tau)$ if the vertex set of $G$ can be partitioned into $D_0\\cup... \\cup D_t$ such that $D_0=M$ and for any $i\\geq 1$ and any $v\\in D_i$, the number of edges from $D_0\\cup... \\cup D_{i-1}$ to $v$ is at least $\\tau(v)$. One of the most applicable and widely studied threshold assignments in directed graphs is strict majority threshold a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.3682","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"}