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arXiv · 2009.12697

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

Lior Gishboliner
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Abstract

We show that if the degree sequence of a graph $G$ is close in $\ell_1$-distance to a given realizable degree sequence $(d_1,\dots,d_n)$, then $G$ is close in edit distance to a graph with degree sequence $(d_1,\dots,d_n)$. 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 $n$.

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Lior Gishboliner. 2020-09-26. Modifying a Graph's Degree Sequence and the Testablity of Degree Sequence Properties. https://arxiv.org/abs/2009.12697

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