✦ LIBER ✦

On large sets of almost Hamilton cycle decompositions

✍ Scribed by Hongtao Zhao; Qingde Kang

Publisher: John Wiley and Sons
Year: 2007
Tongue: English
Weight: 158 KB
Volume: 16
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.20134

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

A large set of CS(v, k, λ), k‐cycle system of order v with index λ, is a partition of all k‐cycles of K~v~ into CS(v, k, λ)s, denoted by LCS(v, k, λ). A (v − 1)‐cycle is called almost Hamilton. The completion of the existence spectrum for LCS(v, v − 1, λ) only depends on one case: all v ≥ 4 for λ = 2. In this article, it is shown that there exists an LCS(v, v − 1,2) for any v ≡ 0,1 (mod 4) except v = 5, and for v = 6,7,10,11. © 2006 Wiley Periodicals, Inc. J Combin Designs 16: 53–69, 2008

📜 SIMILAR VOLUMES

On large sets of Pk-decompositions

✍ Yanfang Zhang 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 81 KB 👁 1 views

Let G ¼ ðVðGÞ; EðGÞÞ be a graph. A ðv v v; G; Þ-GD is a partition of all the edges of LGD. In this paper, we obtain a general result by using the finite fields, that is, if q ! k ! 2 is an odd prime power, then there exists a ðq; P k ; k À 1Þ-LGD.

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

On large sets of resolvable and almost r

On large sets of resolvable and almost resolvable oriented triple systems

✍ Qingde Kang; Jianguo Lei 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 430 KB 👁 1 views

An MTS(v) [or DTS(v)] is said to be resolvable, denoted by RMTS(v) [or RDTS(v)], if its block set can be partitioned into parallel classes. An MTS(v) [or DTS(v)] is said to be almost resolvable, denoted by ARMTS(v) [or ARDTS(v)], if its bloak set can be partitioned into almost parallel classes. The

Maximal sets of Hamilton cycles inKn,n

✍ Bryant, Darryn E.; El-Zanati, S.; Rodger, C. A. 📂 Article 📅 2000 🏛 John Wiley and Sons 🌐 English ⚖ 271 KB

In this article, we prove that there exists a maximal set of m Hamilton cycles in K n,n if and only if n/4 < m ≤ n/2.

Large set of P3-decompositions

✍ Qingde Kang; Yanfang Zhang 📂 Article 📅 2002 🏛 John Wiley and Sons 🌐 English ⚖ 113 KB

## Abstract Let __G__=(__V__(__G__),__E__(__G__)) be a graph. A (__n__,__G__, λ)‐__GD__ is a partition of the edges of λ__K__~__n__~ into subgraphs (__G__‐blocks), each of which is isomorphic to __G__. The (__n__,__G__,λ)‐__GD__ is named as graph design for __G__ or __G__‐decomposition. The large s

Symmetric Hamilton cycle decompositions

Symmetric Hamilton cycle decompositions of complete graphs minus a 1-factor

✍ Richard A. Brualdi; Michael W. Schroeder 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 190 KB 👁 1 views

Let n ≥ 2 be an integer. The complete graph K n with a 1-factor F removed has a decomposition into Hamilton cycles if and only if n is even. We show that K n -F has a decomposition into Hamilton cycles which are symmetric with respect to the 1-factor F if and only if n ≡ 2,4 mod 8. We also show that