Cycles in graphs without proper subgraphs of minimum degree 3

@inproceedings{ErdsCyclesIG,
title={Cycles in graphs without proper subgraphs of minimum degree 3},
author={Paul Erdős and Ralph J. Faudree and Andr{\'a}s Gy{\'a}rf{\'a}s and R. H. SCIIELP}
}

Let G(n,m) denote the set of graphs with n vertices and m edges. It is well-known that each G c G(n,2n-2) contains a subgraph of minimum degree 3 but there exists a G cG(n,2n-3) with no subgraphs of minimum degree 3 (see [1] p. xvü). It was proved in ~2] that each G e G(n, 2n-1) contains a proper subgraph of minimum degree 3, but there exists G cG(n, 2n-2) without this property. In fact, a stronger result was proved in [2], namely that GcG(n,2n-1) must contain a subgraph of minimum degree 3… CONTINUE READING