scholarly journals Decomposition into Cycles I: Hamilton Decompositions

1990 ◽  
pp. 9-18 ◽  
Author(s):  
B. Alspach ◽  
J.-C. Bermond ◽  
D. Sotteau
Keyword(s):  
Hamilton Decompositions

scholarly journals Counting Hamilton Decompositions of Oriented Graphs

2017 ◽  
Vol 2018 (22) ◽  
pp. 6908-6933 ◽  
Author(s):  
Asaf Ferber ◽  
Eoin Long ◽  
Benny Sudakov
Keyword(s):  
Oriented Graphs ◽  
Hamilton Decompositions

scholarly journals Hamilton decompositions of one-ended Cayley graphs

2020 ◽  
Vol 140 ◽  
pp. 171-191
Author(s):  
Joshua Erde ◽  
Florian Lehner ◽  
Max Pitz
Keyword(s):  
Cayley Graphs ◽  
Hamilton Decompositions

scholarly journals Approximate Hamilton Decompositions of Robustly Expanding Regular Digraphs

2013 ◽  
Vol 27 (3) ◽  
pp. 1372-1409 ◽  
Author(s):  
Deryk Osthus ◽  
Katherine Staden
Keyword(s):  
Hamilton Decompositions

scholarly journals Hamilton decompositions of graphs with primitive complements

2009 ◽  
Vol 309 (14) ◽  
pp. 4883-4888 ◽  
Author(s):  
Sibel Ozkan ◽  
C.A. Rodger
Keyword(s):  
Hamilton Decompositions

scholarly journals Optimal Bounds for Disjoint Hamilton Cycles in Star Graphs

2018 ◽  
Vol 29 (03) ◽  
pp. 377-389 ◽  
Author(s):  
Parisa Derakhshan ◽  
Walter Hussak
Keyword(s):  
Interconnection Network ◽  
Multiple Edge ◽  
Star Graph ◽  
Hamilton Cycles ◽  
Star Graphs ◽  
Edge Disjoint ◽  
Spanning Subgraph ◽  
Optimal Bounds ◽  
Hamilton Decompositions ◽  
Hamilton Decomposition

In interconnection network topologies, the [Formula: see text]-dimensional star graph [Formula: see text] has [Formula: see text] vertices corresponding to permutations [Formula: see text] of [Formula: see text] symbols [Formula: see text] and edges which exchange the positions of the first symbol [Formula: see text] with any one of the other symbols. The star graph compares favorably with the familiar [Formula: see text]-cube on degree, diameter and a number of other parameters. A desirable property which has not been fully evaluated in star graphs is the presence of multiple edge-disjoint Hamilton cycles which are important for fault-tolerance. The only known method for producing multiple edge-disjoint Hamilton cycles in [Formula: see text] has been to label the edges in a certain way and then take images of a known base 2-labelled Hamilton cycle under different automorphisms that map labels consistently. However, optimal bounds for producing edge-disjoint Hamilton cycles in this way, and whether Hamilton decompositions can be produced, are not known for any [Formula: see text] other than for the case of [Formula: see text] which does provide a Hamilton decomposition. In this paper we show that, for all n, not more than [Formula: see text], where [Formula: see text] is Euler’s totient function, edge-disjoint Hamilton cycles can be produced by such automorphisms. Thus, for non-prime [Formula: see text], a Hamilton decomposition cannot be produced. We show that the [Formula: see text] upper bound can be achieved for all even [Formula: see text]. In particular, if [Formula: see text] is a power of 2, [Formula: see text] has a Hamilton decomposable spanning subgraph comprising more than half of the edges of [Formula: see text]. Our results produce a better than twofold improvement on the known bounds for any kind of edge-disjoint Hamilton cycles in [Formula: see text]-dimensional star graphs for general [Formula: see text].

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