# The tunnel number of all 11 and 12 crossing alternating knots

## TL;DR

This paper computes the tunnel number for all alternating and some non-alternating knots with 11 and 12 crossings, providing comprehensive data on their topological complexity.

## Contribution

It offers the first complete calculation of tunnel numbers for all 11 and 12 crossing alternating knots and a large class of Montesinos knots, expanding knot theory databases.

## Key findings

- Computed tunnel numbers for 1655 alternating 11 and 12 crossing knots.
- Determined tunnel numbers for 881 non-alternating 11 and 12 crossing knots.
- Identified all 5525 Montesinos knots with up to 14 crossings.

## Abstract

Using exhaustive techniques and results from Lackenby and many others, we compute the tunnel number of all 1655 alternating 11 and 12 crossing knots and of 881 non-alternating 11 and 12 crossing knots. We also find all 5525 Montesinos knots with 14 crossings or fewer.