3‐connected graphs with non‐cut contractible edge covers of size k

In this paper, we show that if a 3‐connected graph G other than K 4 has a vertex subset K that covers the set of contractible edges of G and if | K | 3 and | V(G) | 3| K | − 1, then K is a cutset of G . We also give examples to show that this result is best possible. In particular, the result does not hold for K with smaller cardinality.