Existence of Dλ-cycles and Dλ-paths

H.J. Veldman

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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.
Original languageEnglish
Pages (from-to)309-316
JournalDiscrete mathematics
Issue number3
Publication statusPublished - 1983


  • IR-69241


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