Characterizing degree-sum maximal nonhamiltonian bipartite graphs

In 1963, Moon and Moser gave a bipartite analogue to Ore’s famed theorem on hamiltonian graphs. While the sharpness examples of Ore’s Theorem have been independently characterized in at least four different papers, no similar characterization exists for the Moon–Moser Theorem. In this note, we give such a characterization, consisting of one infinite family and two exceptional graphs of order eight.