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Disjoint Hamilton cycles in transposition graphs

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journal contribution
posted on 04.03.2016, 09:15 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.



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Discrete Applied Mathematics


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


AM (Accepted Manuscript)

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This paper was accepted for publication in the journal Discrete Applied Mathematics and the definitive published version is available at