Every connected, locally connected nontrivial graph with no induced claw is hamiltonian
David J. Oberly, David P. Sumner · Journal of Graph Theory · 1979
Abstract A graph is locally connected if every neighborthood induces a connected subgraph. We show here that every connected, locally connected graph on p ≥ 3 vertices and having no induced K1,3 is Hamiltonian. Several sufficient conditions for a line graph to be Hamiltonian are obtained as corollaries.