On n-stars in colorings and orientations of graphs

• Date: 2016
• Main Author: Protasov, Igor Vladimirovich
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2016
• Subjects: n-star; coloring; orientation.; 2010 MSC: 05C55
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/308
• Journal Title: Algebra and Discrete Mathematics

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...