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doi:10.1016/0012-365X(83)90196-6 
Copyright © 1983 Published by Elsevier Science B.V. All rights reserved.
Existence of Dλ-cycles and Dλ-paths
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H. J. Veldman
Received 4 March 1982;
revised 28 May 1982.
Available online 22 July 2002.
Abstract
A cycle of C of a graph G is called a Dλ-cycle if every component of G − V(C) has order less than λ. A Dλ-path is defined analogously. In particular, a D1-cycle is a hamiltonian cycle and a D1-path is a hamiltonian path. Necessary conditions and sufficient conditions are derived for graphs to have a Dλ-cycle or Dλ-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.
