Alspach has conjectured that any 2k-regular connected Cayley graph cay(A,S) on a finite abelian group A can be decomposed into k hamiltonian cycles. In this paper, the conjecture is shown to be true if S= {sl,sz, s3} is a minimal generating set of A with 1 Al odd, or S={sl,s& . . . . sk} is a genera
Hamiltonian decomposition of Cayley graphs of degree 4
β Scribed by J.-C Bermond; O Favaron; M Maheo
- Publisher
- Elsevier Science
- Year
- 1989
- Tongue
- English
- Weight
- 592 KB
- Volume
- 46
- Category
- Article
- ISSN
- 0095-8956
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Alspach has conjectured that any 2k-regular connected Cayley graph cay(A, S) on a finite abelian group A can be decomposed into k hamiltonian cycles. In this paper, the conjecture is shown to be true if S=[s 1 , s 2 , ..., s k ] is a minimal generating set of an abelian group A of odd order (where a
Alspach has conjectured that any 2k-regular connected Cayley graph cay(A,S) on a finite abelian group A can be decomposed into k hamiltonian cycles. In this paper we generalize a result by Kotzig that the Cartesian product of any two cycles can be decomposed into two hamiltonian cycles and show that
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
## Abstract For any __d__β©Ύ5 and __k__β©Ύ3 we construct a family of Cayley graphs of degree __d__, diameter __k__, and order at least __k__((__d__β3)/3)^__k__^. By comparison with other available results in this area we show that our family gives the largest currently known Cayley graphs for a wide ra