关于3-γ-临界图的Hamilton性

On Hamiltonian Properties of 3-γ-critical Graphs

设ap→b是无终点的3－γ－临界图G的一条Hamiltonian路，文［3］证明了当d（a，b）＝3时，G是Hamiltonian图．本文进一步研究3－γ－临界图的Hamilton性，得到如下结果：如果d（a，b）＝2且｜T｜＝1或T＝N（a）∩N＋（b），则G是Hamiltonian图．这里，T＝V（G）－［N（a）∪N（b）∪｛a，b｝］．

Let ap→ b be a Hamiltonian path of 3-γ-critical graph without endpoints. The paper[3] has proved that if d(a,b ) = 3, then G is a Hamiltonian graph. We further study Hamiltonian properties of 3-γ-critical graphs and obtain that if d(a,b) = 2 with ｜T｜=1 or T = N-(a)∩N+(b), then G is a Hamiltonian graph. where T = V(C) - [N(a)∪N(b)∪{a,b}].