{"paper":{"title":"Graph Coloring and Function Simulation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ali Reza Rahimi, Amir Daneshgar, Siamak Taati","submitted_at":"2010-08-18T05:21:55Z","abstract_excerpt":"We prove that every partial function with finite domain and range can be effectively simulated through sequential colorings of graphs. Namely, we show that given a finite set $S=\\{0,1,\\ldots,m-1\\}$ and a number $n \\geq \\max\\{m,3\\}$, any partial function $\\varphi:S^{^p} \\to S^{^q}$ (i.e. it may not be defined on some elements of its domain $S^{^p}$) can be effectively (i.e. in polynomial time) transformed to a simple graph $\\matr{G}_{_{\\varphi,n}}$ along with three sets of specified vertices $$X = \\{x_{_{0}},x_{_{1}},\\ldots,x_{_{p-1}}\\}, \\ \\ Y = \\{y_{_{0}},y_{_{1}},\\ldots,y_{_{q-1}}\\}, \\ \\ R = "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.3015","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"}