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Title: Disjoint Hamilton cycles in transposition graphs
Authors: Hussak, Walter
Keywords: Transposition graphs
Star graphs
Edge-disjoint Hamilton cycles
Issue Date: 2016
Citation: HUSSAK, W., 2016. Disjoint Hamilton cycles in transposition graphs. Discrete Applied Mathematics, 206, pp. 56-64.
Abstract: Most network topologies that have been studied have been subgraphs of transposition graphs. Edge-disjoint Hamilton cycles are important in network topologies for improving fault-tolerance and distribution of messaging traffic over the network. Not much was known about edge-disjoint Hamilton cycles in general transposition graphs until recently Hung produced a construction of 4 edge-disjoint Hamilton cycles in the 5-dimensional transposition graph and showed how edge-disjoint Hamilton cycles in (n + 1)-dimensional transposition graphs can be constructed inductively from edge-disjoint Hamilton cycles in n-dimensional transposition graphs. In the same work it was conjectured that n-dimensional transposition graphs have n − 1 edge-disjoint Hamilton cycles for all n greater than or equal to 5. In this paper we provide an edge-labelling for transposition graphs and, by considering known Hamilton cycles in labelled star subgraphs of transposition graphs, are able to provide an extra edge-disjoint Hamilton cycle at the inductive step from dimension n to n + 1, and thereby prove the conjecture.
Description: This paper was accepted for publication in the journal Discrete Applied Mathematics and the definitive published version is available at http://dx.doi.org/10.1016/j.dam.2016.02.007.
Version: Accepted for publication
DOI: 10.1016/j.dam.2016.02.007
URI: https://dspace.lboro.ac.uk/2134/20458
Publisher Link: http://dx.doi.org/10.1016/j.dam.2016.02.007
ISSN: 0166-218X
Appears in Collections:Published Articles (Computer Science)

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