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.
Original language | English |
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Pages (from-to) | 309-316 |
Journal | Discrete mathematics |
Volume | 44 |
Issue number | 3 |
DOIs | |
Publication status | Published - 1983 |
Keywords
- IR-69241