𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Hamiltonian decompositions of strong products

✍ Scribed by Fan, Cong; Liu, Jiuqiang

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
286 KB
Volume
29
Category
Article
ISSN
0364-9024

No coin nor oath required. For personal study only.

✦ Synopsis

It is shown that if both G 1 and G 2 are Hamiltonian decomposable, then so is their strong product.

πŸ“œ SIMILAR VOLUMES

Hamiltonian threshold for strong product
Hamiltonian threshold for strong products of graphs
✍ Daniel KrΓ‘l'; Ladislav Stacho πŸ“‚ Article πŸ“… 2008 πŸ› John Wiley and Sons 🌐 English βš– 161 KB

## Abstract We prove that the strong product of any at least ${({\rm ln}}\, {2})\Delta+{O}(\sqrt{\Delta})$ non‐trivial connected graphs of maximum degree at most Ξ” is pancyclic. The obtained result is asymptotically best possible since the strong product of ⌊(ln 2)__D__βŒ‹ stars __K__~1,__D__~ is not

Hamilton decompositions of cartesian pro
Hamilton decompositions of cartesian products of multicycles
✍ Mellendorf, Stephen πŸ“‚ Article πŸ“… 1997 πŸ› John Wiley and Sons 🌐 English βš– 320 KB

We define the multicycle C (r) m as a cycle on m vertices where each edge has multiplicity r. So C (r) m can be decomposed into r Hamilton cycles. We provide a complete answer to the following question: for which positive integers m, n, r, s with m, n β‰₯ 3 can the Cartesian product of two multicycles

Hamiltonian Decompositions of Cayley Gra
Hamiltonian Decompositions of Cayley Graphs on Abelian Groups of Odd Order
✍ Jiuqiang Liu πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 380 KB

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

Random Matchings Which Induce Hamilton C
Random Matchings Which Induce Hamilton Cycles and Hamiltonian Decompositions of Random Regular Graphs
✍ Jeong Han Kim; Nicholas C. Wormald πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 215 KB

Select four perfect matchings of 2n vertices, independently at random. We find the asymptotic probability that each of the first and second matchings forms a Hamilton cycle with each of the third and fourth. This is generalised to embrace any fixed number of perfect matchings, where a prescribed set