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...
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| Datum: | 2016 |
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| Sprache: | English |
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Lugansk National Taras Shevchenko University
2016
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| Назва журналу: | Algebra and Discrete Mathematics |
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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 |
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| 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 |
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AT protasovigorvladimirovich onnstarsincoloringsandorientationsofgraphs |
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2025-12-02T15:40:07Z |
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2025-12-02T15:40:07Z |
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1850412156673064960 |