Pairs of forbidden subgraphs and 2-connected supereulerian graphs

Combining our results with a result in [Xiong (2014)], we prove that all 2-connected hourglass-free claw-free graphs G with one of the same forbidden subgraphs above (or additionally δ(G)≥3) are hamiltonian with the same excluded families of graphs. In particular, we prove that every 3-edge-connected claw-free hourglass-free graph that is N2,2,5-free or Z9-free is hamiltonian.