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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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2016
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| Schlagworte: | |
| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/308 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Zusammenfassung: | 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. |
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