{"paper":{"title":"Anti-van der Waerden numbers on Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alex Schulte, Elizabeth Sprangel, Michael Young, Nathan Warnberg, Shanise Walker, Zhanar Berikkyzy","submitted_at":"2018-02-05T16:50:17Z","abstract_excerpt":"In this paper arithmetic progressions on the integers and the integers modulo n are extended to graphs. This allows for the definition of the anti-van der Waerden number of a graph. Much of the focus of this paper is on 3-term arithmetic progressions for which general bounds are obtained based on the radius and diameter of a graph. The general bounds are improved for trees and Cartesian products and exact values are determined for some classes of graphs. Larger k-term arithmetic progressions are considered and a connection between the Ramsey number of paths and the anti-van der Waerden number "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.01509","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"}