Existence of Dλ-cycles and Dλ-paths


Veldman, H.J. (1983) Existence of Dλ-cycles and Dλ-paths. Discrete Mathematics, 44 (3). pp. 309-316. ISSN 0012-365X

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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.
Item Type:Article
Copyright:© 1983 Elsevier Science
Link to this item:http://purl.utwente.nl/publications/69241
Official URL:https://doi.org/10.1016/0012-365X(83)90196-6
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