Abstract: Let
k
and n be positive integers with n³k.Let
G be
a graph of order n,
and suppose that the minimum value of the sum
of the degrees of two nonadjacent distinct
vertices is greater than or equal to n.
Under these assumptions, we show that for any k
distinct vertices v1,
…, vk,there
exist vertex disjoint subgraphs C1,
…, Ckwith
such
that for each
1 £i£k, viÎV(Ci)and
Ciis
a cycle or isomorphic to K1or
K2.
