Dense-graph extension of sparse-graph techniques

Develop methods extending the techniques used for sparse graphs to prove r-EKR results for dense graphs.

Background

The survey records quantitative r-EKR theorems for graphs with bounded maximum or average degree and for several sparse graph families. It explicitly asks whether those methods can be adapted to address dense graphs, where the existing estimates do not apply.

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 Question 1(c), Section 6