## Abstract A group Γ is said to possess a hamiltonian generating set if there exists a minimal generating set Δ for Γ such that the Cayley color graph __D__~Δ~(Γ) is hamiltonian. It is shown that every finite abelian group has a hamiltonian generating set. Certain classes of nonabelian groups are
Hamiltonian circuits in Cayley graphs
✍ Scribed by Dragan Marušič
- Publisher
- Elsevier Science
- Year
- 1983
- Tongue
- English
- Weight
- 268 KB
- Volume
- 46
- Category
- Article
- ISSN
- 0012-365X
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📜 SIMILAR VOLUMES
The main result of this paper is the NP-completeness of the HAMILTONIAN CIRCUIT problem for chordal bipartite graphs. This is proved by a sophisticated reduction from SATISFIABILITY. As a corollary, HAMILTONIAN CIRCUIT is NP-complete for strongly chordal split graphs. On both classes the complexity
It is proven that every connected Cayley graph X , of valency at least three, on a Hamiltonian group is either Hamilton laceable when X is bipartite, or Hamilton connected when X is not bipartite.
Let G be a group generated by X. A Cayley graph ouer G is defined as a graph G(X) whose vertex set is G and whose edge set consists of all unordered pairs [a, b] with a, b E G and am'b E X U X-', where X-t denotes the set (x-t ( .x E X}. When X is a minimal generating set or each element of X is of