{"paper":{"title":"A Simple Algorithm for Coloring m-Clique Holes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Bechir Hamdaoui","submitted_at":"2015-08-27T18:50:53Z","abstract_excerpt":"An m-clique hole is a sequence $\\phi=(\\Phi_1,\\Phi_2,\\dots,\\Phi_m)$ of $m$ distinct cliques such that $|\\Phi_i| \\leq m$ for all $i=1,2,\\ldots,m$, and whose clique graph is a hole on $m$ vertices. That is, $\\phi$ is an m-clique hole if for all $i\\neq j$, $i,j=1,2,\\ldots,m$, $\\Phi_i \\cap \\Phi_{j} \\neq \\emptyset$ if and only if $(j-1)~\\mbox{mod}~m = (j+1)~\\mbox{mod}~m = i~\\mbox{mod}~m$. This paper derives a sufficient and necessary condition on m-colorability of m-clique holes, and proposes a coloring algorithm that colors m-clique holes with exactly m colors."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06967","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"}