The Regularity Lemma with bounded VC Dimension
Henry Towsner
TL;DR
This paper proves a version of Szemeredi's regularity lemma for graphs with bounded VC dimension, achieving doubly exponential bounds on the partition size, which simplifies the general case.
Contribution
It introduces a specialized proof of the regularity lemma for graphs with bounded VC dimension, reducing the complexity of bounds involved.
Findings
Doubly exponential bounds on partition size for graphs with bounded VC dimension
Simplified proof of Szemeredi's regularity lemma in this special case
Extension of regularity lemma applicability to VC dimension constrained graphs
Abstract
We give a proof of Szemeredi's regularity lemma in the special case of a graph with bounded VC dimension and show that it is possible to obtain "merely" doubly exponential bounds on the size of the partition in this case.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Graph Theory Research · Graph theory and applications