Modifying a Graph's Degree Sequence and the Testablity of Degree Sequence Properties

09/26/2020

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by   Lior Gishboliner, et al.

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We show that if the degree sequence of a graph G is close in ℓ_1-distance to a given realizable degree sequence (d_1,…,d_n), then G is close in edit distance to a graph with degree sequence (d_1,…,d_n). We then use this result to prove that every graph property defined in terms of the degree sequence is testable in the dense graph model with query complexity independent of n.