Note: a counterexample to a conjecture of Jackson about hamiltonicity of diregular digraphs

TL;DR

This paper presents a specific 3-regular circulant digraph on 12 vertices that serves as a counterexample to Jackson's conjecture on the hamiltonicity of diregular digraphs, challenging previous assumptions.

Contribution

It provides the first known counterexample to Jackson's conjecture, demonstrating that not all 3-regular diregular digraphs are Hamiltonian.

Findings

Counterexample disproves Jackson's conjecture

3-regular circulant digraph on 12 vertices is non-Hamiltonian

Challenged existing beliefs about diregular digraphs

Abstract

$3$-diregular circulant digraph on $12$ vertices is a counterexample of Jackson's conjecture about hamiltonicity of diregular digraphs