On Collusion-Free Teaching in Planar Graphs
Non-clashing teaching minimizes teaching complexity among models satisfying the Goldman--Mathias collusion-avoidance criterion. While the Vapnik--Chervonenkis dimension (VCdim) measures the complexity of learning from samples, non-clashing teaching dimension (NCTD) measures the number of examples required when a teacher can select them. Whether NCTD is always bounded above by VCdim remains a fundamental open question in learning theory. In this paper, we investigate this question for the concept classes of closed neighborhoods in planar graphs. We prove a tight upper bound of two on their NCTD, thereby establishing the conjectured inequality for this family. For the positive variant NCTD+...
| Authors | Khazaliya Liana, Kuske Clemens |
|---|---|
| Primary category | cs.DM |
| Published | 13 October 2026 |
| Last updated at source | 13 October 2026 |
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