The ropelength conjecture of alternating knots (Q6652494)

This is a short paper relying on the author's prior work on the ropelength problem. A long standing conjecture states that the ropelength of any alternating knot is at least proportional to its crossing number. In this paper the author proves that this conjecture is true for any alternating knot \(K\). In particular, there is a constant \(b_0 > 1/56\) independent of knot type, such that the ropelength \(R(K) \ge b_0 Cr(K)\) for any alternating knot \(K\) with crossing number \(Cr(K)\). It is important to note that this result only applies to alternating knots,and the ropelength conjecture remains open in general for alternating links with two or more components. In order to fully understand the proof of this result the reader should look at the following two papers by the same author: [J. Knot Theory Ramifications 29, No. 4, Article ID 2050019, 10 p. (2020; Zbl 1439.57009); Algebr. Geom. Topol. 24, No. 5, 2957--2970 (2024; Zbl 07922375)].