ArticleOriginal scientific text
Title
The size of minimum 3-trees: cases 0 and 1 mod 12
Authors 1, 2
Affiliations
- Instituto de Matemáticas, UNAM, Ciudad Universitaria, Circuito exterior, México 04510
- Departamento de Matemáticas, UAM-Iztapalapa, Ave. Sn. Rafael Atlixco #186, Col. Vicentina, México 09340
Abstract
A 3-uniform hypergraph is called a minimum 3-tree, if for any 3-coloring of its vertex set there is a heterochromatic triple and the hypergraph has the minimum possible number of triples. There is a conjecture that the number of triples in such 3-tree is ⎡(n(n-2))/3⎤ for any number of vertices n. Here we give a proof of this conjecture for any n ≡ 0,1 mod 12.
Keywords
tight hypergraphs, triple systems
Bibliography
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Pages:
177-187
Main language of publication
English
Received
2001-11-26
Accepted
2002-05-06
Published
2003
DOI: 10.7151/dmgt.1194
Exact and natural sciences