{"paper":{"title":"Distance-two coloring of sparse graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Louis Esperet, Zdenek Dvorak","submitted_at":"2013-03-13T15:30:23Z","abstract_excerpt":"Consider a graph $G = (V, E)$ and, for each vertex $v \\in V$, a subset $\\Sigma(v)$ of neighbors of $v$. A $\\Sigma$-coloring is a coloring of the elements of $V$ so that vertices appearing together in some $\\Sigma(v)$ receive pairwise distinct colors. An obvious lower bound for the minimum number of colors in such a coloring is the maximum size of a set $\\Sigma(v)$, denoted by $\\rho(\\Sigma)$. In this paper we study graph classes $F$ for which there is a function $f$, such that for any graph $G \\in F$ and any $\\Sigma$, there is a $\\Sigma$-coloring using at most $f(\\rho(\\Sigma))$ colors. It is pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3191","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"}