Corpus ID: 202734360

# 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},
journal={ArXiv},
year={2019},
volume={abs/1909.10701}
}
• Published 2019
• Mathematics, Computer Science
• ArXiv
• 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

#### References

##### Publications referenced by this paper.
SHOWING 1-10 OF 16 REFERENCES

## Partitioning Sparse Graphs into an Independent Set and a Forest of Bounded Degree

• Mathematics, Computer Science
• Electr. J. Comb.
• 2018
VIEW 1 EXCERPT

## Reconfiguring colourings of graphs with bounded maximum average degree

VIEW 1 EXCERPT

## Towards Cereceda's conjecture for planar graphs

• Computer Science, Mathematics
• Journal of Graph Theory
• 2020

## Vertex decompositions of sparse graphs into an independent vertex set and a subgraph of maximum degree at most 1

• Mathematics
• 2011
VIEW 1 EXCERPT

## On the vertex partitions of sparse graphs into an independent vertex set and a forest with bounded maximum degree

• Computer Science, Mathematics
• Appl. Math. Comput.
• 2018
VIEW 1 EXCERPT

## Defective 2-colorings of sparse graphs

• Mathematics, Computer Science
• J. Comb. Theory, Ser. B
• 2014
VIEW 1 EXCERPT

## Maximum average degree and relaxed coloring

• Mathematics, Computer Science
• Discret. Math.
• 2017
VIEW 1 EXCERPT

## On the vertex-arboricity of planar graphs

• Mathematics, Computer Science
• Eur. J. Comb.
• 2008
VIEW 1 EXCERPT

## The point-arboricity of a graph

• Mathematics
• 1968

## Partitioning a Planar Graph of Girth 10 into a Forest and a Matching

VIEW 1 EXCERPT