Hamilton circuits of Cayley graphs of Weyl groupoids of generalized quantum groups

TL;DR

This paper proves the existence of Hamilton circuits in Cayley graphs of Weyl groupoids associated with generalized quantum groups and explicitly constructs such circuits for rank 3 and 4 cases.

Contribution

It establishes the existence of Hamilton circuits in these Cayley graphs and provides explicit examples for low-rank cases, advancing understanding of their combinatorial structure.

Findings

Hamilton circuits exist for all Cayley graphs of Weyl groupoids of generalized quantum groups.

Explicit Hamilton circuits are constructed for rank 3 and 4 cases.

The results connect quantum algebra structures with combinatorial graph properties.

Abstract

We study Hamilton circuits of the Cayley graphs of the Weyl groupoids of the generalized quantum groups, or the quantum double of the Nichols algebras of diagonal-type, with finite root systems. We prove the existence of a Hamilton circuit for any of them and explicitly draw one of them for rank 3 and 4 cases.