On n-stars in colorings and orientations of graphs

An \(n\)-star \(S\) in a graph \(G\) is the union of geodesic intervals \(I _{1} , \ldots , I _{k} \) with common end \(O\) such that the subgraphs \(I_{ 1}\setminus\{O\}, \ldots , I _{k}\setminus\{O\}\) are pairwise disjoint and \(l(I _{1}) +\ldots + l(I _{k})= n.\) If the edges of \(G\) are orient...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Datum:2016
1. Verfasser: Protasov, Igor Vladimirovich
Format: Artikel
Sprache:English
Veröffentlicht: Lugansk National Taras Shevchenko University 2016
Schlagworte:
Online Zugang:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/308
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Назва журналу:Algebra and Discrete Mathematics

Institution

Algebra and Discrete Mathematics
id admjournalluguniveduua-article-308
record_format ojs
spelling admjournalluguniveduua-article-3082016-12-30T22:42:45Z On n-stars in colorings and orientations of graphs Protasov, Igor Vladimirovich n-star, coloring, orientation. 2010 MSC: 05C55 An \(n\)-star \(S\) in a graph \(G\) is the union of geodesic intervals \(I _{1} , \ldots , I _{k} \) with common end \(O\) such that the subgraphs \(I_{ 1}\setminus\{O\}, \ldots , I _{k}\setminus\{O\}\) are pairwise disjoint and \(l(I _{1}) +\ldots + l(I _{k})= n.\) If the edges of \(G\) are oriented, \(S\) is directed if each ray \(I _{i}\) is directed. For natural number \(n, r\), we construct a graph \(G\) of \(\operatorname{diam} (G)=n\) such that, for any \(r\)-coloring and orientation of \(E(G)\), there exists a directed \(n\)-star with monochrome rays of pairwise distinct colors. Lugansk National Taras Shevchenko University 2016-12-31 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/308 Algebra and Discrete Mathematics; Vol 22, No 2 (2016) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/308/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/308/126 Copyright (c) 2016 Algebra and Discrete Mathematics
institution Algebra and Discrete Mathematics
baseUrl_str
datestamp_date 2016-12-30T22:42:45Z
collection OJS
language English
topic n-star
coloring
orientation.
2010 MSC: 05C55
spellingShingle n-star
coloring
orientation.
2010 MSC: 05C55
Protasov, Igor Vladimirovich
On n-stars in colorings and orientations of graphs
topic_facet n-star
coloring
orientation.
2010 MSC: 05C55
format Article
author Protasov, Igor Vladimirovich
author_facet Protasov, Igor Vladimirovich
author_sort Protasov, Igor Vladimirovich
title On n-stars in colorings and orientations of graphs
title_short On n-stars in colorings and orientations of graphs
title_full On n-stars in colorings and orientations of graphs
title_fullStr On n-stars in colorings and orientations of graphs
title_full_unstemmed On n-stars in colorings and orientations of graphs
title_sort on n-stars in colorings and orientations of graphs
description An \(n\)-star \(S\) in a graph \(G\) is the union of geodesic intervals \(I _{1} , \ldots , I _{k} \) with common end \(O\) such that the subgraphs \(I_{ 1}\setminus\{O\}, \ldots , I _{k}\setminus\{O\}\) are pairwise disjoint and \(l(I _{1}) +\ldots + l(I _{k})= n.\) If the edges of \(G\) are oriented, \(S\) is directed if each ray \(I _{i}\) is directed. For natural number \(n, r\), we construct a graph \(G\) of \(\operatorname{diam} (G)=n\) such that, for any \(r\)-coloring and orientation of \(E(G)\), there exists a directed \(n\)-star with monochrome rays of pairwise distinct colors.
publisher Lugansk National Taras Shevchenko University
publishDate 2016
url https://admjournal.luguniv.edu.ua/index.php/adm/article/view/308
work_keys_str_mv AT protasovigorvladimirovich onnstarsincoloringsandorientationsofgraphs
first_indexed 2025-12-02T15:40:07Z
last_indexed 2025-12-02T15:40:07Z
_version_ 1850412156673064960