Analyze f for residue-class edge sequences

Investigate f(n,Kp|F(S)) for the sequences S={1}∪{m:m≡r (mod k)} with r≠1.

Background

Section 7 studies square and selected arithmetic-progression edge-count families. The authors ask for the remaining residue-class sequences of the indicated form.

References

Problem 10.28. Investigate f (n, Kp|F(S)) for the sequences S = S(r, k) = {1} u{m|m=r (mod k)}, where r$1.

— Monochromatic graph decompositions and monochromatic piercing inspired by anti-Ramsey colorings  (2501.09342 - Caro et al., 16 Jan 2025) in Problem 10.28, Section 10.2