A Sufficient Condition of Cyclability
YE Miao-lin · Mathematica Applicata · 2008
We prove the following result:let G=(V,E) be a k-connected graph,k≥2,of order n≥3.Denote by X1,X2,…,Xk subsets of vertex set V and let X=X1∪X2∪…∪Xk.If for each i,i=1,2,…,k,and each pair of nonadjacent vertices u,v∈Xi,we have d(u)+d(v)≥n,or |N(u)∪N(v)|≥n-δ or |N(u)∩N(v)|≥α,where δ is minimum degree of G and α is independent number of G,then G is X-cyclable.