Show that if $\chi (G) >2k$ then $G$ contains a $k-$connected subgraph.
In graphs of large chromatic number, I studied a recent paper on the extension on the fact: "that every graph of chromatic number at least $4k + 1$ contains a subgraph of connectivity at least $k$ " result by [W. Mader]. https://arxiv.org/pdf/2004.00533.pdf But I am stuck on this problem. Any hint or help is appreciated. Thanks in advance.