{"paper":{"title":"Coloring clique-hypergraph of $K_5$-minor-free graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Erfang Shan, Liying Kang, Yuxiao Sun","submitted_at":"2014-08-18T08:50:55Z","abstract_excerpt":"A clique-coloring of a graph $G$ is a coloring of the vertices of $G$ so that no maximal clique of size at least two is monochromatic. The clique-hypergraph, $\\mathcal{H}(G)$, of a graph $G$ has $V(G)$ as its set of vertices and the maximal cliques of $G$ as its hyperedges. A (vertex) coloring of $\\mathcal{H}(G)$ is a clique-coloring of $G$. The clique-chromatic number of $G$ is the least number of colors for which $G$ admits a clique-coloring. Every planar graph has been proved to be 3-clique-colorable (Electr. J. Combin. 6 (1999), \\#R26). Recently, we showed that every claw-free planar graph"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3935","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"}