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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| Date: | 2016 |
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| Format: | Article |
| Language: | English |
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Lugansk National Taras Shevchenko University
2016
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/308 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543034167001088 |
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| author | Protasov, Igor Vladimirovich |
| author_facet | Protasov, Igor Vladimirovich |
| author_sort | Protasov, Igor Vladimirovich |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2016-12-30T22:42:45Z |
| 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. |
| first_indexed | 2025-12-02T15:40:07Z |
| format | Article |
| id | admjournalluguniveduua-article-308 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:40:07Z |
| publishDate | 2016 |
| publisher | Lugansk National Taras Shevchenko University |
| 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 |
| spellingShingle | n-star coloring orientation. 2010 MSC: 05C55 Protasov, Igor Vladimirovich On n-stars in colorings and orientations of graphs |
| title | 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_short | On n-stars in colorings and orientations of graphs |
| title_sort | on n-stars in colorings and orientations of graphs |
| topic | n-star coloring orientation. 2010 MSC: 05C55 |
| topic_facet | n-star coloring orientation. 2010 MSC: 05C55 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/308 |
| work_keys_str_mv | AT protasovigorvladimirovich onnstarsincoloringsandorientationsofgraphs |