I'm taking a graph theory course, and we're using West's book Introduction to Graph theory, and I was surprised to see that structural induction is not explicitly discussed, if used at all, typically relying on strong induction to prove results.
Are there any important results in graph theory that are hard (or impossible) to prove without using structural induction? I've seen proofs using structural induction about binary trees in my algorithms and data structures course, so I was also wondering if structural induction in graph theory is usually limited to trees, and if not, what other graph-based structures we can use it prove things about.