Long paths through four vertices in a 2‐connected graph

Let G be a 2‐connected graph, let u and v be distinct vertices in V(G), and let X be a set of at most four vertices lying on a common (u, v)‐path in G. If deg(x) ≥ d for all x ∈ V(G) \ {u, v}, then there is a (u, v)‐path P in G with X ? V(P) and |E(P)| ≥ d. © 2000 John Wiley & Sons, Inc. J Graph Theory 33: 55–65, 2000