Smaller subgraphs of minimum degree k

Frank Mousset, Andreas Noever, Nemanja Škorić

Research output: Contribution to journalArticlepeer-review


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

Original languageEnglish
Article number#P4.9
JournalElectronic Journal of Combinatorics
Issue number4
StatePublished - 6 Oct 2017
Externally publishedYes


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