Any link has a diagram with only triangles and quadrilaterals

TL;DR

This paper proves that every link can be represented by a diagram composed solely of triangular and quadrilateral regions, extending previous related results.

Contribution

It establishes that any link admits a diagram with only triangles and quadrilaterals, broadening the understanding of link diagram structures.

Findings

Every link has a diagram with only triangles and quadrilaterals

Extends previous results by the authors and C. Adams

Provides a new class of simplified link diagrams

Abstract

A link diagram can be considered as a $4$-valent graph embedded in the $2$-sphere and divides the sphere into complementary regions. In this paper, we show that any link has a diagram with only triangles and quadrilaterals. This extends previous results shown by the authors and C. Adams.