L(G)是Hamiltonian的一个充分条件

A sufficient condition for L(G) to be Hamiltonian

设G是n≥3阶几乎无桥的连通图,G■K1,n-1,M=abc1c2c3是五个点的路,Bi={a,b,ci,ci+1},i=1,2,V1=V(G)-V(M).若对G中任何同构于M的导出子图满足下列条件之一:(ⅰ)■x0∈V1,|N〈bi〉(x0)|≥3,i=1,2;(ⅱ)xm∈V1,m=1,…,i+1(xs≠xt;s≠t;s,t=1,…,i+1),∑i+1m=1|N〈Bi〉(xm)|≥2i,i=1,2.则G有一个D-闭迹,从而L(G)是Hamiltonian.

Let G be a connected almost bridgeless graph of order n≥3,G K1,n-1,Mabc1 c2 c3 is a path of five vetex,let Bi{a,b,c1,ci＋1},i1,2;V1V（G）-V（M）.Such the every induced subgraph isomorphic M satisfies at leat one of the following conditions： （ⅰ） x0∈V1,｜N〈bi〉（x0）｜≥3,i1,2; （ⅱ）Arbitary xm∈V1,m1,…,i＋1（xs≠xt;s≠t;s,t1,…,i＋1）,i＋1↑∑↑m=1｜N（xm）｜≥2i,i1,2. Then L（G） is Hamiltonian.