Sparse-method extension to dense graphs

Develop modifications of the techniques used for sparse graphs that establish the r-EKR property for suitable dense graphs.

Background

The paper surveys degree-based results that prove the EKR property for sparse graphs over specified ranges of r. It explicitly asks whether those methods can be adapted to graphs with high density.

References

Might the techniques applied to sparse graphs be tweaked somewhat so as to work for dense graphs?

— A Survey of the Holroyd-Talbot Conjecture  (2501.16144 - Hurlbert, 27 Jan 2025) in Section 6, Questions and Remarks, item 1(c)