Investigate edge connectivity in piercing problems

Investigate the role of edge connectivity in g(n,G|H) for graphs H that admit a bipartite anti-packer inside G.

Background

Theorem 9.37 and Remark 9.38 indicate that graphs with different edge-connectivity properties exhibit different subquadratic piercing behavior. The authors leave the systematic theory undeveloped.

References

Problem 10.12. Investigate the role of edge connectivity number in the context of g(n, G|H) for graphs H which admit a bipartite anti-packer inside G.

— Monochromatic graph decompositions and monochromatic piercing inspired by anti-Ramsey colorings  (2501.09342 - Caro et al., 16 Jan 2025) in Problem 10.12, Section 10.1