Decreasing the maximum average degree by deleting an independent set or a ddegenerate subgraph
Abstract
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 $(k1)$degenerate. Moreover, such $S$ can be computed in polynomial time. In particular there exists an independent set $I$ in $G$ such that $\mathrm{mad}(GI) \le \mathrm{mad}(G)1$ and an induced forest $F$ such that $\mathrm{mad}(GF) \le \mathrm{mad}(G)  2$.
 Publication:

arXiv eprints
 Pub Date:
 September 2019
 DOI:
 10.48550/arXiv.1909.10701
 arXiv:
 arXiv:1909.10701
 Bibcode:
 2019arXiv190910701N
 Keywords:

 Computer Science  Discrete Mathematics;
 Mathematics  Combinatorics