TY - JOUR
A2 - da Fonseca, C.
A2 - Wu, B.
A2 - Godbole, A. P.
A2 - Kiliç, E.
A2 - Bannai, E.
AU - Mészáros, Tamás
AU - Rónyai, Lajos
PY - 2013
DA - 2013/02/27
TI - Shattering-Extremal Set Systems of Small VC-Dimension
SP - 126214
VL - 2013
AB - We say that a set system ℱ⊆2[n] shatters a given set S⊆[n] if 2S={F∩S:F∈ℱ}. The Sauer inequality states that in general, a set system ℱ shatters at least |ℱ| sets. Here, we concentrate on the case of equality. A set system is called shattering-extremal if it shatters exactly |ℱ| sets. We characterize shattering extremal set systems of Vapnik-Chervonenkis dimension 1 in terms of their inclusion graphs. Also, from the perspective of extremality, we relate set systems of bounded Vapnik-Chervonenkis dimension to their projections.
SN - null
UR - https://doi.org/10.1155/2013/126214
DO - 10.1155/2013/126214
JF - ISRN Combinatorics
PB - Hindawi Publishing Corporation
KW -
ER -