## A proof of a conjecture by Erdős, Faudree, Rousseau, and Schelp about subgraphs of minimum degree k. arXiv:1705.09979, 2017. the electronic journal of combinatorics

- L. Sauermann
- 2017

@article{Mousset2017SmallerSO, title={Smaller Subgraphs of Minimum Degree \$k\$}, author={Frank Mousset and Andreas Noever and Nemanja Skoric}, journal={Electr. J. Comb.}, year={2017}, volume={24}, pages={P4.9} }

- Published in Electr. J. Comb. 2017

In 1990, Erdős, Faudree, Rousseau and Schelp proved that for k > 2 every graph with n > k+ 1 vertices and (k− 1)(n−k+ 2) + ( k−2 2 ) + 1 edges contains a subgraph of minimum degree k on at most n − √ n/6k3 vertices. They conjectured that it is possible to remove at least kn many vertices and remain with a subgraph of minimum degree k, for some k > 0. We make progress towards their conjecture by showing that one can remove at least Ω(n/ log n) many vertices.