有关Hamilton图与连通度的一个充分条件

One new sufficient condition for hamilton graphs

利用插点方法和H序列,证明了如果G是n阶简单图,κ=κ(G)≥k≥2.而(a1,a2,…,ak+1)是H序列.若对于任意的Y∈I(ke+)1(G),有∑k+1i=1aisi(Y)+sk+1(Y)>n+κ+k-3,则G是Hamilton图.该定理也是对这方面已有的某些定理的有效推广.

Using the vertex inserting method and the concept of H- sequence, one new sufficient condition for Hamilton graphs is proved. If G is the simple graph on n vertices, k =k （G）≥k≥2. In addition （a1,a2,...,ak＋1） is the H-sequence. For any Y∈I（k＋1）^（e）（G）,if∑i=1^（k＋1）aisi（ Y） ＋ sk＋l（ Y） 〉 n ＋k ＋ k - 3 ,then G is Hamiltonian. This theorem is the effective popularization of relevant theorems in this aspect.