Abstract
A cycle of C of a graph G is called a D λ -cycle if every component of G − V( C) has order less than λ. A D λ -path is defined analogously. In particular, a D 1-cycle is a hamiltonian cycle and a D 1-path is a hamiltonian path. Necessary conditions and sufficient conditions are derived for graphs to have a D λ -cycle or D λ -path. The results are generalizations of theorems in hamiltonian graph theory. Extensions of notions such as vertex degree and adjacency of vertices to subgraphs of order greater than 1 arise in a natural way.
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