{"paper":{"title":"Arbitrary Overlap Constraints in Graph Packing Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Alejandro L\\'opez-Ortiz, Jazm\\'in Romero","submitted_at":"2016-01-14T17:31:55Z","abstract_excerpt":"In earlier versions of the community discovering problem, the overlap between communities was restricted by a simple count upper-bound [17,5,11,8]. In this paper, we introduce the $\\Pi$-Packing with $\\alpha()$-Overlap problem to allow for more complex constraints in the overlap region than those previously studied. Let $\\mathcal{V}^r$ be all possible subsets of vertices of $V(G)$ each of size at most $r$, and $\\alpha: \\mathcal{V}^r \\times \\mathcal{V}^r \\to \\{0,1\\}$ be a function. The $\\Pi$-Packing with $\\alpha()$-Overlap problem seeks at least $k$ induced subgraphs in a graph $G$ subject to: ("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.03676","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"}