Symmetry breaking in tournaments

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dc.contributor	Universitat Politècnica de Catalunya. Departament de Llenguatges i Sistemes Informàtics
dc.contributor	Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions
dc.contributor.author	Lozano Bojados, Antoni
dc.date	2010
dc.identifier.citation	Lozano, A. "Symmetry breaking in tournaments". 2010.
dc.identifier.uri	http://hdl.handle.net/2117/91158
dc.language.iso	eng
dc.relation	LSI-10-19-R
dc.rights	info:eu-repo/semantics/openAccess
dc.subject	Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
dc.subject	Tournament
dc.subject	Determining number
dc.subject	Metric dimension
dc.title	Symmetry breaking in tournaments
dc.type	info:eu-repo/semantics/publishedVersion
dc.type	info:eu-repo/semantics/report
dc.description.abstract	We provide upper bounds for the determining number and the metric dimension of tournaments. A set of vertices S is a determining set for a tournament T if every nontrivial automorphism of T moves at least one vertex of S, while S is a resolving set for T if every two distinct vertices in T have different distances to some vertex in S. We show that the minimum size of a determining set for an order n tournament (its determining number) is bounded by n/3, while the minimum size of a resolving set for an order n strong tournament (its metric dimension) is bounded by n/2. Both bounds are optimal.