Characterising Bounded Expansion by Neighbourhood Complexity
نویسندگان
چکیده
We show that a graph class G has bounded expansion if and only if it has bounded r-neighbourhood complexity, i.e. for any vertex set X of any subgraph H of G ∈ G, the number of subsets of X which are exact r-neighbourhoods of vertices of H on X is linear to the size of X. This is established by bounding the r-neighbourhood complexity of a graph in terms of both its r-centred colouring number and its weak r-colouring number, which provide known characterisations to the property of bounded expansion.
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عنوان ژورنال:
- CoRR
دوره abs/1603.09532 شماره
صفحات -
تاریخ انتشار 2016