2134/20458
Walter Hussak
Disjoint Hamilton cycles in transposition graphs
2016
Loughborough University
Transposition graphs
Star graphs
Edge-disjoint Hamilton cycles
Automorphisms
2016-03-04 09:15:24
article
https://repository.lboro.ac.uk/articles/journal_contribution/Disjoint_Hamilton_cycles_in_transposition_graphs/9402743
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.