New chromatic numbers in open problems |
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| Author |
i.v.protasov@gmail.com
Department of Cybernetics, Kyiv University
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| Abstract |
Given a graph G and a natural number r, we use all possible r-colorings of V (G) and
E(G) to introduce chromatic path numbers and chromatic diameters of G. Replacing colorings
of E(G) with orientations, we define directed path numbers and directed diameter of G. We
formulate 7 open problems.
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| Keywords |
chromatic path number; chromatic diameter; directed path number; directed diameter
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| DOI |
doi:10.15330/ms.45.2.115-117
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| Reference |
1. T. Banakh, A. Idzik, I. Protasov, K. Pszczola, Isometric copies of directed trees in orientations of graphs,
preprint (http://arxiv.org/abs/1606.01973).
2. R. Graham, B. Rothschild, J. Spencer, Ramsey Theory, Wiley, New York, 1990. 3. I. Kohayakawa, T. Luczak, V. Rodl, Ramsey-type results for oriented trees, J. Graph Theory, 22 (1996), ¹1, 1–8. 4. I. Protasov, On n-stars in colorings and orientations of graphs, preprint (www.researchgate.net/project/On-n-stars-in-colorings-and-orientations-of-graphs). |
| Pages |
115-117
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| Volume |
45
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| Issue |
2
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| Year |
2016
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| Journal |
Matematychni Studii
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| Full text of paper | |
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