Smaller Subgraphs of Minimum Degree $k$

@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}
}
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. 

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