{"paper":{"title":"Distinguishing locally finite trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hannah Schreiber, Judith Kloas, Svenja H\\\"uning, Thomas W. Tucker, Wilfried Imrich","submitted_at":"2018-10-04T15:03:01Z","abstract_excerpt":"The distinguishing number $D(G)$ of a graph $G$ is the smallest number of colors that is needed to color the vertices of $G$ such that the only color preserving automorphism is the identity. For infinite graphs $D(G)$ is bounded by the supremum of the valences, and for finite graphs by $\\Delta(G)+1$, where $\\Delta(G)$ is the maximum valence. Given a finite or infinite tree $T$ of bounded finite valence $k$ and an integer $c$, where $2 \\leq c \\leq k$, we are interested in coloring the vertices of $T$ by $c$ colors, such that every color preserving automorphism fixes as many vertices as possible"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.02265","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"}