Symmetry breaking in tournaments

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 diff...

Descripción completa

Detalles Bibliográficos
Autor: Lozano Boixadors, Antoni|||0000-0002-3633-063X
Tipo de recurso: informe técnico
Fecha de publicación:2010
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/91158
Acceso en línea:https://hdl.handle.net/2117/91158
Access Level:acceso abierto
Palabra clave:Tournament
Determining number
Metric dimension
Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
Descripción
Sumario: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.