Extend the theory beyond complete target graphs

Develop the generalized anti-Ramsey theory for graphs H other than complete graphs and for families H containing multiple graphs rather than a single graph.

Background

The paper studies the functions f(n,G|F) and g(n,G|F) predominantly when the target graph G is a complete graph Kp. The authors identify extending the framework to arbitrary target graphs and richer target families as a natural next step.

References

Problem 10.1. (i) Develop the general theory to the involvement of graphs H other than complete graphs. (ii) Develop the theory to the involvement of families H of graphs richer than a single graph H.

— Monochromatic graph decompositions and monochromatic piercing inspired by anti-Ramsey colorings  (2501.09342 - Caro et al., 16 Jan 2025) in Problem 10.1, Section 10