{"paper":{"title":"Threshold Colorings of Prisms and the Petersen Graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gasper Fijavz, Matthias Kriesell","submitted_at":"2016-08-08T06:38:10Z","abstract_excerpt":"Let $G$ be a graph, $r \\geq t$ integers, and $N \\subseteq E(G)$. An $(r,t)$-threshold-coloring of $G$ with respect to $N$ is a mapping $c: V(G) \\rightarrow \\{0,\\ldots,r-1\\}$ such that $|c(u)-c(v)| \\leq t$ for every $uv \\in N$ and $|c(u)-c(v)|>t$ for every $uv \\in E(G) \\setminus N$. A graph is total threshold colorable if there exist integers $r,t$ such that for every $N \\subseteq E(G)$, $G$ admits an $(r,t)$-threshold-coloring with respect to $N$. We show that every prism is total threshold colorable, and that the Petersen graph is total threshold colorable. In contrast to this fact we show th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.02332","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"}