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

Lior Gishboliner

paper

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

arXiv:2009.12697

Abstract

We show that if the degree sequence of a graph $G$ is close in $ℓ_{1}$ -distance to a given realizable degree sequence $(d_{1}, \dots, d_{n})$ , 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 $n$ .