Longest cycles in 3‐connected graphs contain three contractible edges
Nathaniel Dean, Robert L. Hemminger, Katsuhiro Ota · Journal of Graph Theory · 1989
Abstract We show that if G is a 3‐connected graph of order at least seven, then every longest path between distinct vertices in G contains at least two contractible edges. An immediate corollary is that longest cycles in such graphs contain at least three contractible edges.