Bipartite knots

TL;DR

This paper addresses a specific open problem in topology by providing a solution that confirms the existence of knots without matched diagrams, advancing understanding in knot theory.

Contribution

It offers a solution to a longstanding open problem, demonstrating the existence of certain knots that lack matched diagrams.

Findings

Confirmed the existence of knots without matched diagrams

Provided a positive answer to Przytycki's 1987 conjecture

Solved a part of Kirby's Problem 1.60 in topology

Abstract

We give a solution to a part of Problem 1.60 in Kirby's list of open problems in topology thus answering in the positive the 1987 conjecture by J.Przytycki concerning the existence of knots without matched diagrams.