原图是平面图的4-连通线图的哈密尔顿连通性（英文）

Hamiltonicity of 4-connected Line Graph of a Planar Graph

对于一个整数.s≥0,如果图G的任何一个点子集S (?) V(G)满足|S|≤s,并且G-S是哈密尔顿的,那么称图G是s-哈密尔顿的.本文证明原图是平面图的4-连通线图是2-哈密尔顿的并且还是哈密尔顿连通的.这一结果推广了赖虹建在[Graph and Combinatorics,1994, 10:249-253]中的结果.

For an integer s≥0,a graph G is s-Hamiltonian if for any vertex subset S C.V(G)with|S|≤s,(7-S is Hamiltonian.In this note,we show that every 4-connected line graph of a planar graph is 2-Haimltonian,and it is also Hamiltonian-connected.These results generalize work of Lai in[Graph and Combinatorics,1994,10:249-253].