# Decreasing maximum average degree by deleting independent set or d-degenerate subgraph

@article{Nadara2019DecreasingMA, title={Decreasing maximum average degree by deleting independent set or d-degenerate subgraph}, author={Wojciech Nadara and Marcin Smulewicz}, journal={ArXiv}, year={2019}, volume={abs/1909.10701} }

The maximum average degree $\mathrm{mad}(G)$ of a graph $G$ is the maximum average degree over all subgraphs of $G$. In this paper we prove that for every $G$ and positive integer $k$ such that $\mathrm{mad}(G) \ge k$ there exists $S \subseteq V(G)$ such that $\mathrm{mad}(G - S) \le \mathrm{mad}(G) - k$ and $G[S]$ is $(k-1)$-degenerate. Moreover, such $S$ can be computed in polynomial time. In particular there exists an independent set $I$ in $G$ such that $\mathrm{mad}(G-I) \le \mathrm{mad}(G… CONTINUE READING

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