Let H be a class of given graphs. A graph G is said to be H-free if G contains no induced copies of H for any H∈H. In this article, we characterize all pairs {R,S} of graphs such that every connected {R,S}-free graph has the same edge-connectivity and minimum degree.
@article{arxiv.1711.08890,
title = {Forbidden pairs for equality of edge-connectivity and minimum degree},
author = {Junfeng Du and Ziwen Huang and Liming Xiong},
journal= {arXiv preprint arXiv:1711.08890},
year = {2017}
}