Non-clashing teaching dimension versus VC dimension for finite concept classes

Determine whether the non-clashing teaching dimension nctd(C) is at most the VapnikChervonenkis dimension VCdim(C) for every finite binary concept class C.

Background

The paper studies the conjectured inequality nctd(C) VCdim(C) for concept classes consisting of closed neighborhoods in planar graphs. It proves the inequality for this graph-based family by establishing a tight upper bound of two on the non-clashing teaching dimension. The general finite-concept-class case remains unresolved, so extending the planar-graph result to arbitrary finite binary concept classes is explicitly identified as an open problem.