Structural scope of the isometric-cycle approach

Characterize the broader graph classes for which a minimum cycle basis algorithm restricted to isometric cycles necessarily yields an integral cycle basis.

Background

The paper notes that the minimum integral cycle basis problem is solvable on planar graphs by applying a minimum cycle basis algorithm over isometric cycles, because isometric cycle bases are integral in planar graphs. It explicitly identifies as unresolved the task of determining how far this algorithmic approach extends beyond planar graphs, with the goal of delimiting the structural boundary of the known polynomial-time method.

References

For instance, while the minimum integral cycle basis problem can be solved on planar graphs using Horton's algorithm over isometric cycles , the broader graph classes for which this algorithmic approach remains valid are unknown.

— Characterizations and Complexity of Minimum Forward and Integer Cycle Bases  (2609.02317 - Riccardi et al., 2 Sep 2026) in Section 1, Introduction