A graph G is H-free if any subset of V(G) does not induce a subgraph of G that is isomorphic to H. Given a graph H, we present sufficient and necessary conditions for a graph G such that G/e is H-free for any edge e in E(G). Thereafter, we use these conditions to characterize forests, claw-free, 2K2-free, C4-free, C5-free, split, and pseudo-split graphs.
@article{arxiv.2203.03491,
title = {Edge Contraction and Forbidden Induced Graphs},
author = {Hany Ibrahim and Peter Tittmann},
journal= {arXiv preprint arXiv:2203.03491},
year = {2022}
}