New Upper Bounds on the Ribbonlength of Alternating Links with Bipartite Dual Graphs

Fuente: arXiv
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Main Author: Yoo, Hyungkee
Format: Preprint
Published: 2026
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author Yoo, Hyungkee
author_facet Yoo, Hyungkee
contents The ribbonlength of a link is a geometric invariant defined as the infimum of the ratio of the length to the width of a folded ribbon realization of the link. In this paper, we prove that if an alternating link admits an alternating diagram with a bipartite dual graph, then its ribbonlength satisfies $$ \mathrm{Rib}(L) \le \sqrt{3} \, c(L). $$ Using this result, we present improved upper bounds on the ribbonlength for several knots and links with small crossing numbers, and determines the exact ribbonlength of the Hopf link to be $2\sqrt{3}$.
format Preprint
id arxiv_https___arxiv_org_abs_2601_10278
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle New Upper Bounds on the Ribbonlength of Alternating Links with Bipartite Dual Graphs
Yoo, Hyungkee
Geometric Topology
The ribbonlength of a link is a geometric invariant defined as the infimum of the ratio of the length to the width of a folded ribbon realization of the link. In this paper, we prove that if an alternating link admits an alternating diagram with a bipartite dual graph, then its ribbonlength satisfies $$ \mathrm{Rib}(L) \le \sqrt{3} \, c(L). $$ Using this result, we present improved upper bounds on the ribbonlength for several knots and links with small crossing numbers, and determines the exact ribbonlength of the Hopf link to be $2\sqrt{3}$.
title New Upper Bounds on the Ribbonlength of Alternating Links with Bipartite Dual Graphs
topic Geometric Topology
url https://arxiv.org/abs/2601.10278