# A short note on graphs with long Thomason's chains

## TL;DR

This paper introduces a family of 3-connected cubic planar Hamiltonian graphs that require an exponentially large number of steps for Thomason's algorithm, with a base exceeding previous known results.

## Contribution

It constructs a new family of graphs demonstrating exponential complexity for Thomason's algorithm, surpassing earlier bounds.

## Key findings

- Exponential lower bound with base ~1.1812 for Thomason's algorithm on these graphs
- New family of graphs with specific connectivity and planarity properties
- Improved understanding of algorithmic complexity in graph theory

## Abstract

We present a family of 3-connected cubic planar Hamiltonian graphs with an exponential number of steps required by Thomason's algorithm. The base of the exponent is approximately $1.1812...$, which exceeds previous results in the area.