RTD-Conjecture and Concept Classes Induced by Graphs
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916613021761536 |
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| author | Simon, Hans U. |
| author_facet | Simon, Hans U. |
| contents | It is conjectured that the recursive teaching dimension of any finite concept class is upper-bounded by the VC-dimension of this class times a universal constant. In this paper, we confirm this conjecture for two rich families of concept classes where each class is induced by some graph $G$. For each $G$, we consider the class whose concepts represent stars in $G$ as well as the class whose concepts represent connected sets in $G$. We show that, for concept classes of this kind, the recursive teaching dimension either equals the VC-dimension or is less by $1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_09453 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | RTD-Conjecture and Concept Classes Induced by Graphs Simon, Hans U. Discrete Mathematics 68R05 (primary) 05C99 (secondary) F.1.3; G.2.1; I.2.6 It is conjectured that the recursive teaching dimension of any finite concept class is upper-bounded by the VC-dimension of this class times a universal constant. In this paper, we confirm this conjecture for two rich families of concept classes where each class is induced by some graph $G$. For each $G$, we consider the class whose concepts represent stars in $G$ as well as the class whose concepts represent connected sets in $G$. We show that, for concept classes of this kind, the recursive teaching dimension either equals the VC-dimension or is less by $1$. |
| title | RTD-Conjecture and Concept Classes Induced by Graphs |
| topic | Discrete Mathematics 68R05 (primary) 05C99 (secondary) F.1.3; G.2.1; I.2.6 |
| url | https://arxiv.org/abs/2502.09453 |