Abstract: Ewa·Wojcicka [1] has proved that the connected 3 γ critical graphs has a H path and has put forward to such a conjecture: Connected 3 γ critical graphs without endpoints are H graphs. In this paper,we prove that if G is a connected 3 γ critical graph without endpoints and has a Hpaht ap →a such that d(a,b)=3, then G is a H graph. The result partially solves Ewa. Wojcicka's conjecture. 

Key words:  , 3-γ-critical graph；H-path；H-cycle；H-graph