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 ρ(T)...
| Author: | |
|---|---|
| Format: | Article |
| Publication date: | 2019 |
| 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:2117/180131 |
| Online Access: | https://hdl.handle.net/2117/180131 |
| Access Level: | Open access |
| Keyword: | Graph theory Grafs, Teoria de Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica |
| Summary: | 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. |
|---|