On n-stars in colorings and orientations of graphs
An n-star S in a graph G is the union of geodesic intervals I1,…,Ik with common end O such that the subgraphs I1∖{O},…,Ik∖{O} are pairwise disjoint and l(I1)+…+l(Ik)=n. If the edges of G are oriented, S is directed if each ray Ii is directed. For natural number n,r, we construct a graph G of diam(G)...
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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2016 |
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| Language: | English |
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Інститут прикладної математики і механіки НАН України
2016
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/155731 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On n-stars in colorings and orientations of graphs / I.V. Protasov // Algebra and Discrete Mathematics. — 2016. — Vol. 22, № 2. — С. 301-303. — Бібліогр.: 3 назв. — англ. |
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Protasov, I.V. 2019-06-17T11:29:56Z 2019-06-17T11:29:56Z 2016 On n-stars in colorings and orientations of graphs / I.V. Protasov // Algebra and Discrete Mathematics. — 2016. — Vol. 22, № 2. — С. 301-303. — Бібліогр.: 3 назв. — англ. 1726-3255 2010 MSC:05C55. https://nasplib.isofts.kiev.ua/handle/123456789/155731 An n-star S in a graph G is the union of geodesic intervals I1,…,Ik with common end O such that the subgraphs I1∖{O},…,Ik∖{O} are pairwise disjoint and l(I1)+…+l(Ik)=n. If the edges of G are oriented, S is directed if each ray Ii is directed. For natural number n,r, we construct a graph G of 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. I thank Taras Banakh and Oleg Pikhurko for infosupport and discussions roundabout this note. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On n-stars in colorings and orientations of graphs Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
On n-stars in colorings and orientations of graphs |
| spellingShingle |
On n-stars in colorings and orientations of graphs Protasov, I.V. |
| 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 |
| author |
Protasov, I.V. |
| author_facet |
Protasov, I.V. |
| publishDate |
2016 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| description |
An n-star S in a graph G is the union of geodesic intervals I1,…,Ik with common end O such that the subgraphs I1∖{O},…,Ik∖{O} are pairwise disjoint and l(I1)+…+l(Ik)=n. If the edges of G are oriented, S is directed if each ray Ii is directed. For natural number n,r, we construct a graph G of 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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| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/155731 |
| citation_txt |
On n-stars in colorings and orientations of graphs / I.V. Protasov // Algebra and Discrete Mathematics. — 2016. — Vol. 22, № 2. — С. 301-303. — Бібліогр.: 3 назв. — англ. |
| work_keys_str_mv |
AT protasoviv onnstarsincoloringsandorientationsofgraphs |
| first_indexed |
2025-12-02T07:04:00Z |
| last_indexed |
2025-12-02T07:04:00Z |
| _version_ |
1850861813319598080 |