We prove that every finite 4-connected graph G has at least 1 34 · (|E(G)| − 2|V (G)|) many contractible edges. AMS subject classification: 05c40, 05c35.

We study the distribution of small contractible subgraphs in 3-connected graphs under local regularity conditions. AMS classification: 05c40, 05c75, 05c35.