The smallest 5-chromatic tournament
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F24%3A00144081" target="_blank" >RIV/00216224:14330/24:00144081 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1090/mcom/3887" target="_blank" >https://doi.org/10.1090/mcom/3887</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1090/mcom/3887" target="_blank" >10.1090/mcom/3887</a>
Alternative languages
Result language
angličtina
Original language name
The smallest 5-chromatic tournament
Original language description
A coloring of a digraph is a partition of its vertex set such that each class induces a digraph with no directed cycles. A digraph is k-chromatic if k is the minimum number of classes in such partition, and a digraph is oriented if there is at most one arc between each pair of vertices. Clearly, the smallest k-chromatic digraph is the complete digraph on k vertices, but determining the order of the smallest k-chromatic oriented graphs is a challenging problem. It is known that the smallest 2-, 3- and 4-chromatic oriented graphs have 3, 7 and 11 vertices, respectively. In 1994, Neumann-Lara conjectured that a smallest 5-chromatic oriented graph has 17 vertices. We solve this conjecture and show that the correct order is 19.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
MATHEMATICS OF COMPUTATION
ISSN
0025-5718
e-ISSN
1088-6842
Volume of the periodical
93
Issue of the periodical within the volume
345
Country of publishing house
US - UNITED STATES
Number of pages
16
Pages from-to
443-458
UT code for WoS article
001028974200001
EID of the result in the Scopus database
2-s2.0-85174950088