On k-ordered graphs
Article first published online: 8 SEP 2000
Copyright © 2000 John Wiley & Sons, Inc.
Journal of Graph Theory
Volume 35, Issue 2, pages 69–82, October 2000
How to Cite
Faudree, J. R., Faudree, R. J., Gould, R. J., Jacobson, M. S. and Lesniak, L. (2000), On k-ordered graphs. J. Graph Theory, 35: 69–82. doi: 10.1002/1097-0118(200010)35:2<69::AID-JGT1>3.0.CO;2-I
- Issue published online: 8 SEP 2000
- Article first published online: 8 SEP 2000
- Manuscript Received: 18 DEC 1998
- O.N.R.. Grant Numbers: N00014-91-J-1085 (RJF), N00014-97-1-0499 (RJG), N00014-91-J-1098 (MSJ), N00014-J-93-1-0050 (LL).
- degree sum;
- k-ordered Hamiltonian;
- neighborhood union
Ng and Schultz [J Graph Theory 1 (1997), 45–57] introduced the idea of cycle orderability. For a positive integer k, a graph G is k-ordered if for every ordered sequence of k vertices, there is a cycle that encounters the vertices of the sequence in the given order. If the cycle is also a Hamiltonian cycle, then G is said to be k-ordered Hamiltonian. We give sum of degree conditions for nonadjacent vertices and neighborhood union conditions that imply a graph is k-ordered Hamiltonian. © 2000 John Wiley & Sons, Inc. J Graph Theory 35: 69–82, 2000