Cactus graphs satisfy the strong bunkbed conjecture, and any graph satisfies the conjecture if and only if all of its biconnected components do.
The complexity of some edge deletion problems
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The bunkbed conjecture still holds for cactus graphs and for graphs with certain biconnected components
Cactus graphs satisfy the strong bunkbed conjecture, and any graph satisfies the conjecture if and only if all of its biconnected components do.