摘要
设H为一图.H中由m个点组成的独立集和由m个点组成的割集分别称为m-独立集和m-割集,而经过v∈V（H）的圈v-圈.设D为H的子图,测|D|和H-D分别表示|V（D）|（D的阶）和H-V（D）.称H是无爪的,如果它不含K1,3作为导出子图.称H是m-路连通的（m≥1）,如果|H|≥2,H的任一对点都由长度≥m的路相联.称只有一个点的图为0-路连通的.H中的路R是一dominating路,如果R是Hamilton的,或者V（H-R）是一独立点集.对H的子图A和D。
If F is a ( k - 1)-connected( k≥2)claw-free graph of order n ,and if the degree sum≥n - k +1 for any ( k +1) -independent set { υ1, …υk+1}, then any longest path in F is dominating, i. e. every edge of F has at least one endvertex on this path. If { υ,ν} V(F) is not included in any (vertex) cut-set of k vertices in a k -connected ( k ≥ 2 ) claw-free graph F of order n ,and if the degree sum of any ( k + 1 )-independent set which contains neither υ nor ν is at least n - k + 2, while the degree sum of any ( k + 1 )-independent set containing only one of a and v is at least n + 1 ,then any longest ( υ,ν )-path is Hamiltonian.
出处
《高校应用数学学报（A辑）》
CSCD
北大核心
1992年第2期315-316,共2页
Applied Mathematics A Journal of Chinese Universities(Ser.A)
