𝔖 Bobbio Scriptorium
✦   LIBER   ✦

The Hamilton—Waterloo problem: The case of triangle-factors and one Hamilton cycle

✍ Scribed by J.H. Dinitz; Alan C.H. Ling

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
166 KB
Volume
17
Category
Article
ISSN
1063-8539

No coin nor oath required. For personal study only.

✦ Synopsis

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 consider the case when R is a triangle‐factor, S is a Hamilton cycle and s__=__1. We solve the problem completely except for 14 possible exceptions. This solves a major open case from the 2004 article of Horak et al. © 2008 Wiley Periodicals, Inc. J Combin Designs 17: 160–176, 2009

📜 SIMILAR VOLUMES

The Hamilton-Waterloo problem for Hamilt
The Hamilton-Waterloo problem for Hamilton cycles and triangle-factors
✍ Hongchuan Lei; Hao Shen 📂 Article 📅 2011 🏛 John Wiley and Sons 🌐 English ⚖ 147 KB

## 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)

The Hamilton–Waterloo problem for cycle
The Hamilton–Waterloo problem for cycle sizes 3 and 4
✍ Peter Danziger; Gaetano Quattrocchi; Brett Stevens 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 127 KB

## 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

Hamilton-connectivity and cycle-embeddin
Hamilton-connectivity and cycle-embedding of the Möbius cubes
✍ Jianxi Fan 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 68 KB

The recently introduced interconnection network, the Möbius cube, is an important variant of the hypercube. This network has several attractive properties compared with the hypercube. In this paper, we show that the n-dimensional Möbius cube M n is Hamilton-connected when n 3. Then, by using the Ham

On the number of hamilton cycles in a ra
On the number of hamilton cycles in a random graph
✍ C. Cooper; A. M. Frieze 📂 Article 📅 1989 🏛 John Wiley and Sons 🌐 English ⚖ 576 KB

Let a random graph G be constructed by adding random edges one by one, starting with n isolated vertices. We show that with probability going to one as n goes to infinity, when G first has minimum degree two, it has at least (log n)('-')" distinct hamilton cycles for any fixed E > 0.

Symmetric Hamilton cycle decompositions
Symmetric Hamilton cycle decompositions of the complete graph
✍ Jin Akiyama; Midori Kobayashi; Gisaku Nakamura 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 95 KB 👁 1 views

## Abstract We construct a new symmetric Hamilton cycle decomposition of the complete graph __K~n~__ for odd __n__ > 7. © 2003 Wiley Periodicals, Inc.