Intersecting families in unions of cycle powers

Determine whether disjoint unions of powers of cycles are r-EKR for values of r other than the maximum independent-set size covered by the known theorem.

Background

The survey explains that Hilton, Holroyd, and Spencer proved the r-EKR property for disjoint unions of cycle powers when r equals the independence number and at least one component is a simple cycle. They also identified the maximum centers in that case.

The remaining values of r for such unions were explicitly identified as unresolved at that point in the survey.