Large highly connected subgraphs in graphs with linear average degree

Abstract

In 1972 Mader proved that every graph with average degree at least $4k$ has a $(k+1)$-connected subgraph with more than $2k$ vertices. We improve this bound by showing that the constant $4$ can be replaced by $3+\frac{1}{3}$; this bound is sharp.

References in corpus (2)

• On the number of edges in a graph with no $(k+1)$-connected subgraphs
• Minimal Connectivity