{"paper":{"title":"Is there any polynomial upper bound for the universal labeling of graphs?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Ali Dehghan, Arash Ahadi, Morteza Saghafian","submitted_at":"2017-01-23T23:49:48Z","abstract_excerpt":"A {\\it universal labeling} of a graph $G$ is a labeling of the edge set in $G$ such that in every orientation $\\ell$ of $G$ for every two adjacent vertices $v$ and $u$, the sum of incoming edges of $v$ and $u$ in the oriented graph are different from each other. The {\\it universal labeling number} of a graph $G$ is the minimum number $k$ such that $G$ has {\\it universal labeling} from $\\{1,2,\\ldots, k\\}$ denoted it by $\\overrightarrow{\\chi_{u}}(G) $. We have $2\\Delta(G)-2 \\leq \\overrightarrow{\\chi_{u}} (G)\\leq 2^{\\Delta(G)}$, where $\\Delta(G)$ denotes the maximum degree of $G$. In this work, w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06685","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"}