  In this article, we generalize the classification of genus one Lefschetz
fibrations to genus one simplified broken Lefschetz fibrations, which have
fibers of genera one and zero. We classify genus one Lefschetz fibrations over
the 2-disk with certain non-trivial global monodromies using chart
descriptions, and identify the 4-manifolds admitting genus one simplified
broken Lefschetz fibrations.
