Distinguishing tournaments with small label classes
A d-distinguishing vertex (arc) labeling of a digraph is a vertex (arc) labeling using d labels that is not preserved by any nontrivial automorphism. Let ρ(T) (ρ′(T)) be the minimum size of a label class in a 2-distinguishing vertex (arc) labeling of a tournament T. Gluck's Theorem implies that...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2019 |
| 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:2117/180131 |
| Acceso en línea: | https://hdl.handle.net/2117/180131 |
| Access Level: | acceso abierto |
| Palabra clave: | Graph theory Grafs, Teoria de Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica |
| Sumario: | A d-distinguishing vertex (arc) labeling of a digraph is a vertex (arc) labeling using d labels that is not preserved by any nontrivial automorphism. Let ρ(T) (ρ′(T)) be the minimum size of a label class in a 2-distinguishing vertex (arc) labeling of a tournament T. Gluck's Theorem implies that ρ(T) ≤ ⌊n/2⌋ for any tournament T of order n. We construct a family of tournaments ℌ such that ρ(T) ≥ ⌊n/2⌋ for any tournament of order n in ℌ. Additionally, we prove that ρ′(T) ≤ ⌊7n/36⌋ + 3 for any tournament T of order n and ρ′(T) ≥ ⌈n/6⌉ when T ∈ ℌ and has order n. These results answer some open questions stated by Boutin. |
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