{"paper":{"title":"Explicit 3-colorings for exponential graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Adrien Argento, Alantha Newman, Pierre Charbit","submitted_at":"2018-08-27T05:40:01Z","abstract_excerpt":"For a graph $H$ and integer $k \\geq 1$, two functions $f, g$ from $V(H)$ into $\\{1, \\dots, k\\}$ are adjacent if for all edges $uv$ of $H$, $f(u) \\neq g(v)$. The graph of all such functions is the exponential graph $K_k^H$. El-Zahar and Sauer proved that if $\\chi(H) \\geq 4$, then $K_3^H$ is 3-chromatic. Tardif showed that, implicit in their proof, is an algorithm for 3-coloring $K_3^H$ whose time complexity is polynomial in the size of $K_3^H$. Tardif then asked if there is an \"explicit\" algorithm for finding such a coloring: Essentially, given a function $f$ belonging to a 3-chromatic componen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.08691","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"}