Pivot Gray codes for broader graph families

Establish the existence of pivot Gray code constructions for graph families broader than the currently treated classes, including efficient listings in which consecutive graph objects differ by the prescribed local pivot operation.

Background

The paper studies cyclic pivot Gray codes for well-ordered k-degenerate graphs, where consecutive graphs differ by adding, deleting, or pivoting a single edge. It places this construction in the broader context of pivot Gray codes for spanning trees and related graph structures.

Although prior work had established pivot Gray codes for several specific families, including fan graphs, outerplanar graphs, complete graphs, and tournament arborescences, the paper states that existence for broader graph families is unresolved. The cited examples of graph classes with previously posed questions are described as having subsequently been settled in the surrounding discussion, so the unresolved issue retained here is the general existence problem for broader families.