Cycle Extendability in Graphs, Bigraphs and Digraphs
Document Type
Presentation
Journal/Book Title/Conference
42nd Southeastern International Conference on Combinatorics, Graph Theory, and Computing, Boca Raton, FL
Publication Date
2011
Abstract
In 1990, Hendry conjectured that all chordal Hamiltonian graphs are cycle extendable, that is, the vertices of each non-Hamiltonian cycle are contained in a cycle of length one greater. In this talk, we discuss some preliminary results on a generalization of the concept of cycle- extendability to S-extendable; that is, with S ⊆ {1, 2, . . . , n} and G a graph on n vertices, G is S-extendable if the vertices of every non-Hamiltonian cycle are contained in a cycle length i greater, where i ∈ S. We present some results on tournaments, i.e., complete directed graphs, and some observations about cycle-extendability and S-extendability for non-directed graphs.
Recommended Citation
Beasley, LeRoy B.; Brown, David E.; and Thomas, Brent, "Cycle Extendability in Graphs, Bigraphs and Digraphs" (2011). Mathematics and Statistics Faculty Presentations. Paper 36.
https://digitalcommons.usu.edu/mathsci_presentations/36