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The 3 and 4-dichromatic tournaments of minimum order

✍ Scribed by V. Neumann-Lara

Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 630 KB
Volume: 135
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(93)e0113-i

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✦ Synopsis

The dichromatic number k(D) of a digraph D is the minimum number of acyclic sets in which V(D) can be partitioned. If de(D) = Y, D is said r-dichromatic. In this paper it is proved that the minimum order of a 3-dichromatic (resp. 4-dichromatic) tournament is 7 (resp. 11). It is also proved that there are exactly four nonisomorphic 3-dichromatic tournaments of order 7 and a unique 4-dichromatic tournament of order 11. All these tournaments are characterized.

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