{"paper":{"title":"Odd Yao-Yao Graphs are Not Spanners","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Jian Li, Wei Zhan, Yifei Jin","submitted_at":"2017-04-11T03:50:11Z","abstract_excerpt":"It is a long standing open problem whether Yao-Yao graphs $\\mathsf{YY}_{k}$ are all spanners [li2002sparse]. Bauer and Damian [bauer2013infinite] showed that all $\\mathsf{YY}_{6k}$ for $k \\geq 6$ are spanners. Li and Zhan [li2016almost] generalized their result and proved that all even Yao-Yao graphs $\\mathsf{YY}_{2k}$ are spanners (for $k\\geq 42$). However, their technique cannot be extended to odd Yao-Yao graphs, and whether they are spanners are still elusive. In this paper, we show that, surprisingly, for any integer $k \\geq 1$, there exist odd Yao-Yao graph $\\mathsf{YY}_{2k+1}$ instances,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03132","kind":"arxiv","version":4},"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"}