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
On Hamiltonian Decompositions of Cayley Graphs on Cyclic Groups
โ Scribed by YIXIU HUANG
- Book ID
- 119862773
- Publisher
- John Wiley and Sons
- Year
- 1989
- Tongue
- English
- Weight
- 234 KB
- Volume
- 576
- Category
- Article
- ISSN
- 0890-6564
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๐ SIMILAR VOLUMES
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
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.