Frankl's conjecture for bipartite graphs with pendant vertices

Let $G$ be a bipartite graph, and call a vertex pendant when it has degree one. Frankl's pendant-vertex conjecture. Every bipartite graph with at least one pendant vertex satisfies Frankl's conjecture. The source places this among graph-theoretic formulations equivalent to the union-closed sets conjecture; it is consequently open in general, while the paper proves related statements for particular graph structures.