{"paper":{"title":"Folding graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Ton Kloks, Yue-Li Wang","submitted_at":"2012-07-04T09:37:06Z","abstract_excerpt":"Let G be a graph. Consider two nonadjacent vertices x and y that have a common neighbor. Folding G with respect to x and y is the operation which identifies x and y. After a maximal series of foldings the graph is a disjoint union of cliques. The minimal clique number that can appear after a maximal series of foldings is equal to the chromatic number of G. In this paper we consider the problem to determine the maximal clique number which can appear after a maximal series of foldings. We denote this number as Sigma(G) and we call it the max-folding number. We show that the problem is NP-complet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.0932","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"}