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arXiv · 1703.00273

Smaller subgraphs of minimum degree k

Frank Mousset·Andreas Noever·Nemanja Škorić
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Abstract

In 1990 Erdős, Faudree, Rousseau and Schelp proved that for $k\geq 2$, every graph with $n\geq k+1$ vertices and $(k-1)(n-k+2)+\binom{k-2}{2}+1$ edges contains a subgraph of minimum degree $k$ on at most $n-\sqrt{n}/\sqrt{6k^3}$ vertices. They conjectured that it is possible to remove at least $ε_k n$ many vertices and remain with a subgraph of minimum degree $k$, for some $ε_k>0$. We make progress towards their conjecture by showing that one can remove at least $Ω(n/\log n)$ many vertices.

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Frank Mousset, Andreas Noever, Nemanja Škorić. 2017-03-01. Smaller subgraphs of minimum degree k. https://arxiv.org/abs/1703.00273

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