Hamiltonian path decomposition of fan graphs

This paper focuses on Hamiltonian path decompositions of fan graphs Fm,n which is the join graph \overline{K_m} + P_n where \overline{K_m} is an empty graph with m vertices and Pn is a path with n vertices. It is proved that Fm,n admits a Hamiltonian path decomposition (possibly with a near 1-factor leave) if and only if m = n?1 for all n ? 3. The result is proved make used of the method of graph amalgamations.