• Corpus ID: 246652451

VC-density and abstract cell decomposition for edge relation in graphs of bounded twin-width

  title={VC-density and abstract cell decomposition for edge relation in graphs of bounded twin-width},
  author={Wojciech Przybyszewski},
We study set systems formed by neighborhoods in graphs of bounded twin-width. In particular, we prove that such classes of graphs admit linear neighborhood complexity, in analogy to previous results concerning classes with bounded expansion and classes of bounded clique-width. Additionally, we show how, for a given graph from a class of graphs of bounded twin-width, to efficiently encode the neighborhood of a vertex in a given set of vertices A of the graph. For the encoding we use only a… 

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On the Density of Families of Sets

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