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 |
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Distinguishing tournaments with small label classesLozano Boixadors, Antoni|||0000-0002-3633-063XGraph theoryGrafs, Teoria deÀrees temàtiques de la UPC::Informàtica::Informàtica teòricaA 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.Peer Reviewed20192019-07-3020202020-03-17journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/180131reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)InglésengEuropean Commission http://doi.org/10.13039/100010661 Horizon 2020 Framework Programme 648276 A Unified Theory of Algorithmic Relaxationsopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/1801312026-05-27T15:37:01Z |
| dc.title.none.fl_str_mv |
Distinguishing tournaments with small label classes |
| title |
Distinguishing tournaments with small label classes |
| spellingShingle |
Distinguishing tournaments with small label classes Lozano Boixadors, Antoni|||0000-0002-3633-063X Graph theory Grafs, Teoria de Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica |
| title_short |
Distinguishing tournaments with small label classes |
| title_full |
Distinguishing tournaments with small label classes |
| title_fullStr |
Distinguishing tournaments with small label classes |
| title_full_unstemmed |
Distinguishing tournaments with small label classes |
| title_sort |
Distinguishing tournaments with small label classes |
| dc.creator.none.fl_str_mv |
Lozano Boixadors, Antoni|||0000-0002-3633-063X |
| author |
Lozano Boixadors, Antoni|||0000-0002-3633-063X |
| author_facet |
Lozano Boixadors, Antoni|||0000-0002-3633-063X |
| author_role |
author |
| dc.subject.none.fl_str_mv |
Graph theory Grafs, Teoria de Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica |
| topic |
Graph theory Grafs, Teoria de Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica |
| description |
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. |
| publishDate |
2019 |
| dc.date.none.fl_str_mv |
2019 2019-07-30 2020 2020-03-17 |
| dc.type.none.fl_str_mv |
journal article http://purl.org/coar/resource_type/c_6501 VoR http://purl.org/coar/version/c_970fb48d4fbd8a85 |
| dc.type.openaire.fl_str_mv |
info:eu-repo/semantics/article |
| format |
article |
| dc.identifier.none.fl_str_mv |
https://hdl.handle.net/2117/180131 |
| url |
https://hdl.handle.net/2117/180131 |
| dc.language.none.fl_str_mv |
Inglés eng |
| language_invalid_str_mv |
Inglés |
| language |
eng |
| dc.relation.none.fl_str_mv |
European Commission http://doi.org/10.13039/100010661 Horizon 2020 Framework Programme 648276 A Unified Theory of Algorithmic Relaxations |
| dc.rights.none.fl_str_mv |
open access http://purl.org/coar/access_right/c_abf2 |
| dc.rights.openaire.fl_str_mv |
info:eu-repo/semantics/openAccess |
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open access http://purl.org/coar/access_right/c_abf2 |
| eu_rights_str_mv |
openAccess |
| dc.format.none.fl_str_mv |
application/pdf |
| dc.source.none.fl_str_mv |
reponame:UPCommons. Portal del coneixement obert de la UPC instname:Universitat Politècnica de Catalunya (UPC) |
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Universitat Politècnica de Catalunya (UPC) |
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UPCommons. Portal del coneixement obert de la UPC |
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UPCommons. Portal del coneixement obert de la UPC |
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1869405478892601344 |
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15,300719 |