## Abstract In this article, we consider the Hamilton‐Waterloo problem for the case of Hamilton cycles and triangle‐factors when the order of the complete graph __K__~__n__~ is even. We completely solved the problem for the case __n__≡24 (mod 36). For the cases __n__≡0 (mod 18) and __n__≡6 (mod 36)
On the Hamilton-Waterloo Problem for Bipartite 2-Factors
✍ Scribed by Darryn Bryant; Peter Danziger; Matthew Dean
- Book ID
- 112120489
- Publisher
- John Wiley and Sons
- Year
- 2012
- Tongue
- English
- Weight
- 989 KB
- Volume
- 21
- Category
- Article
- ISSN
- 1063-8539
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
## Abstract The Hamilton—Waterloo problem is to determine the existence of a 2‐factorization of __K__~2__n__+1~ in which __r__ of the 2‐factors are isomorphic to a given 2‐factor __R__ and __s__ of the 2‐factors are isomorphic to a given 2‐factor __S__, with __r__ + __s__=__n__. In this article we
## Abstract The Hamilton–Waterloo problem seeks a resolvable decomposition of the complete graph __K__~__n__~, or the complete graph minus a 1‐factor as appropriate, into cycles such that each resolution class contains only cycles of specified sizes. We completely solve the case in which the resolu
It is shown that if F 1 , F 2 , ...,F t are bipartite 2-regular graphs of order n and 1 , 2 , . . . , t are positive integers such that 1 + 2 +• • •+ t = (n-2) / 2, 1 ≥ 3 is odd, and i is even for i = 2, 3, . . . , t, then there exists a 2-factorization of K n -I in which there are exactly i 2-facto