Frankl's conjecture for bipartite graphs with exactly one pendant vertex

Let $G$ be a bipartite graph, and call a vertex pendant when it has degree one. Frankl's one-pendant-vertex conjecture. Every bipartite graph with exactly one pendant vertex satisfies Frankl's conjecture. The source presents this as one of three graph-theoretic conjectures equivalent to the union-closed sets conjecture; its general status is therefore open, although restricted graph classes are proved in the paper.