I'm searching for results relating to piercing numbers. One example of what I'm looking for is this theorem: any VC Class which is k-consistent has a bounded piercing number.

However, searching Google/arxiv only gives me the above theorem and a bunch of papers about convex sets. What are some other results/papers related to piercing numbers? Ideally, they should be combinatorial in nature as opposed to geometric.

Background: I'm asking this because I'm currently doing research on the possible connection between VC Classes and compression schemes.