{"paper":{"title":"Anagram-free colorings of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Benny Sudakov, Nina Kam\\v{c}ev, Tomasz {\\L}uczak","submitted_at":"2016-06-29T12:12:54Z","abstract_excerpt":"A sequence $S$ is called anagram-free if it contains no consecutive symbols $r_1 r_2\\dots r_k r_{k+1} \\dots r_{2k}$ such that $r_{k+1} \\dots r_{2k}$ is a permutation of the block $r_1 r_2\\dots r_k$. Answering a question of Erd\\H{o}s and Brown, Ker\\\"anen constructed an infinite anagram-free sequence on four symbols.\n  Motivated by the work of Alon, Grytczuk, Ha\\l uszczak and Riordan, we consider a natural generalisation of anagram-free sequences for graph colorings. A coloring of the vertices of a given graph $G$ is called anagram-free if the sequence of colors on any path in $G$ is anagram-fre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.09062","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"}