✦ LIBER ✦

Maximal sets of hamilton cycles in complete multipartite graphs

✍ Scribed by Mike Daven; J. A. MacDougall; C. A. Rodger

Publisher: John Wiley and Sons
Year: 2003
Tongue: English
Weight: 154 KB
Volume: 43
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.10096

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

A set S of edge‐disjoint hamilton cycles in a graph G is said to be maximal if the edges in the hamilton cycles in S induce a subgraph H of G such that G − E(H) contains no hamilton cycles. In this context, the spectrum S(G) of a graph G is the set of integers m such that G contains a maximal set of m edge‐disjoint hamilton cycles. This spectrum has previously been determined for all complete graphs and for all complete bipartite graphs. In this paper, we extend these results to the complete multipartite graphs. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 49–66, 2003

📜 SIMILAR VOLUMES

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.

Maximal independent sets in graphs with

Maximal independent sets in graphs with at most r cycles

✍ Goh Chee Ying; Koh Khee Meng; Bruce E. Sagan; Vincent R. Vatter 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 127 KB 👁 1 views

## Abstract We find the maximum number of maximal independent sets in two families of graphs. The first family consists of all graphs with __n__ vertices and at most __r__ cycles. The second family is all graphs of the first family which are connected and satisfy __n__ ≥ 3__r__. © 2006 Wiley Period

Properly colored hamilton cycles in edge

Properly colored hamilton cycles in edge-colored complete graphs

✍ N. Alon; G. Gutin 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 156 KB 👁 3 views

It is shown that, for ⑀ ) 0 and n ) n ⑀ , any complete graph K on n vertices 0 ' Ž . whose edges are colored so that no vertex is incident with more than 1 y 1r 2 y ⑀ n edges of the same color contains a Hamilton cycle in which adjacent edges have distinct colors. Moreover, for every k between 3 and

Hamilton decompositions of complete mult

Hamilton decompositions of complete multipartite graphs with any 2-factor leave

✍ C. D. Leach; C. A. Rodger 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 85 KB 👁 1 views

## Abstract For __m__ ≥ 1 and __p__ ≥ 2, given a set of integers __s__~1~,…,__s__~__q__~ with $s\_j \geq p+1$ for $1 \leq j \leq q$ and ${\sum \_{j\,=\,1}^q} s\_j = mp$, necessary and sufficient conditions are found for the existence of a hamilton decomposition of the complete __p__‐partite graph $

Decompositions of complete graphs into t

Decompositions of complete graphs into triangles and Hamilton cycles

✍ Darryn Bryant; Barbara Maenhaut 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 121 KB 👁 1 views

## Abstract For all odd integers __n__ ≥ 1, let __G~n~__ denote the complete graph of order __n__, and for all even integers __n__ ≥ 2 let __G~n~__ denote the complete graph of order __n__ with the edges of a 1‐factor removed. It is shown that for all non‐negative integers __h__ and __t__ and all p

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