Resolve the remaining rainbow-clique cases

Determine the inducibility or semi-inducibility extremal constructions for rainbow cliques K_k^{rb} with k in {4,6,7,8,9,10}.

Background

The paper surveys results on rainbow cliques in edge-coloured complete graphs. The cases k>=11 have been resolved asymptotically, while the three-colour rainbow triangle and the five-vertex case behave differently from the general iterated-blow-up construction. The authors explicitly identify the orders 4 and 6 through 10 as the remaining open cases.

References

Thus the remaining open cases are $k \in {4,6,7,8,9,10}$.

— The semi-inducibility problem  (2501.09842 - Basit et al., 16 Jan 2025) in Section 2.2, “The inducibility problem”