{"paper":{"title":"Bisected vertex leveling of plane graphs: braid index, arc index and delta diagrams","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Hyungkee Yoo, Seungsang Oh, Sungjong No","submitted_at":"2018-06-25T22:34:34Z","abstract_excerpt":"In this paper, we introduce a bisected vertex leveling of a plane graph. Using this planar embedding, we present elementary proofs of the well-known upper bounds in terms of the minimal crossing number on braid index $b(L)$ and arc index $\\alpha(L)$ for any knot or non-split link $L$, which are $b(L) \\leq \\frac{1}{2} c(L) + 1$ and $\\alpha(L) \\leq c(L) + 2$. We also find a quadratic upper bound of the minimal crossing number of delta diagrams of $L$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.09719","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"}