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Disjoint Hamilton cycles in transposition graphs

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journal contribution
posted on 04.03.2016 by Walter Hussak
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.

History

School

  • Science

Department

  • Computer Science

Published in

Discrete Applied Mathematics

Citation

HUSSAK, W., 2016. Disjoint Hamilton cycles in transposition graphs. Discrete Applied Mathematics, 206, pp. 56-64.

Version

AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2016

Notes

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.

ISSN

0166-218X

Language

en

Exports