Extend the theory to other graph universes

Develop the generalized anti-Ramsey theory for bipartite graphs, directed graphs, signed graphs, and uniform hypergraphs.

Background

All edge colorings considered in the paper are colorings of complete undirected graphs. The authors point to established extremal theories for restricted or generalized graph settings as motivation for extending their framework.

References

Problem 10.2. Develop the theory for * bipartite graphs; * directed graphs; * signed graphs; * uniform hypergraphs.

Monochromatic graph decompositions and monochromatic piercing inspired by anti-Ramsey colorings  (2501.09342 - Caro et al., 16 Jan 2025) in Problem 10.2, Section 10