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...
| Author: | |
|---|---|
| Format: | report |
| Publication Date: | 2010 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2117/91158 |
| Online Access: | https://hdl.handle.net/2117/91158 |
| Access Level: | Open access |
| Keyword: | Tournament Determining number Metric dimension Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica |
| Summary: | 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. |
|---|