We present a new condition on the degree slims of a graph that implies the existence of a long cycle. Our result is a generalization of the previous one of N.Dean and P.Fraiss.
B.Jackson(参见J.Comb.Theory(B),29(1980),27-46)证明了2连通k正则的图G=(V,E),当点数n≤3k时G有Hamilton圈;在“The improvcment of Jackson’s result on Hamiltonian Cyclesin 2-connected regular graphs”一文中我们改进了Jackson的结果,证明了2连通的k正则图,当n≤3k+1时它有Hamilton圈;本文又进一步证明了2连通k正则的图,当点数不超过3k+3时它有Hamilton圈。
