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Title: Symmetry and optimality of disjoint Hamilton cycles in star graphs
Authors: Derakhshan, Parisa
Hussak, Walter
Keywords: Star graph
Hamilton cycle
Hamilton decomposition
Issue Date: 2014
Publisher: Department of Computer Science, Loughborough University.
Citation: DERAKHSHAN, P. and HUSSAK, W., 2014. Symmetry and optimality of disjoint Hamilton cycles in star graphs. Technical Report 1111. Department Computer Science, Loughborough University.
Abstract: Multiple edge-disjoint Hamilton cycles have been obtained in labelled star graphs Stn of degree n-1, using number-theoretic means, as images of a known base 2-labelled Hamilton cycle under label-mapping auto- morphisms of Stn. However, no optimum bounds for producing such edge-disjoint Hamilton cycles have been given, and no positive or nega- tive results exist on whether Hamilton decompositions can be produced by such constructions other than a positive result for St5. We show that for all even n there exist such collections, here called symmetric collec- tions, of φ(n)/2 edge-disjoint Hamilton cycles, where φ is Euler's totient function, and that this bound cannot be improved for any even or odd n. Thus, Stn is not symmetrically Hamilton decomposable if n is not prime. Our method improves on the known bounds for numbers of any kind of edge-disjoint Hamilton cycles in star graphs.
Description: This is a report.
Sponsor: Department Computer Science, Loughborough University
Version: Published
URI: https://dspace.lboro.ac.uk/2134/19300
Appears in Collections:Technical Reports (Computer Science)

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