The smallest 5-chromatic tournament

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

The smallest 5-chromatic tournament

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

The smallest 5-chromatic tournament

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

MATHEMATICS OF COMPUTATION

ISSN

0025-5718

e-ISSN

1088-6842

Svazek periodika

93

Číslo periodika v rámci svazku

345

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

16

Strana od-do

443-458

Kód UT WoS článku

001028974200001

EID výsledku v databázi Scopus

2-s2.0-85174950088