{"paper":{"title":"A note on the Thue chromatic number of lexicographic products of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrej Taranenko, Erika \\v{S}krabu\\v{l}\\'akov\\'a, Iztok Peterin, Jens Schreyer","submitted_at":"2014-09-17T21:42:09Z","abstract_excerpt":"A sequence is called non-repetitive if no of its subsequences forms a repetition (a sequence $r_1,r_2,\\dots,r_{2n}$ such that $r_i=r_{n+i}$ for all $1\\leq i \\leq n$). Let $G$ be a graph whose vertices are coloured. A colouring $\\varphi$ of the graph $G$ is non-repetitive if the sequence of colours on every path in $G$ is non-repetitive. The Thue chromatic number, denoted by $\\pi (G)$, is the minimum number of colours of a non-repetitive colouring of $G$. In this short note we present a general upper bound for the Thue chromatic number for the lexicographic product $G\\circ H$ of graphs $G$ and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.5154","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"}