The star graph interconnection network has been recognized as an attractive alternative to the popular hypercube network. In this paper, we first address a dual-hamiltonian- path-based (DHPB) routing model with two virtual channels based on two hamiltonian paths and a network partitioning strategy for wormhole-routed star graph networks. Then, we propose three efficient multicast routing schemes on basis of such a model. The proposed schemes are network-selection-based (NSB), heuristic-network- selection-based (HNSB), and two-phase heuristic-network- selection-based (TP-HNSB) dual-path routing. All of the three proposed schemes are deadlock-free. Finally, experimental results are given to show our proposed three routing schemes outperform the unicast-based, the hamiltonian-path, and the single-hamiltonian-path-based (SHPB) dual-path routing schemes significantly.