The size of minimum 3-trees: cases 0 and 1 mod 12

• Autorzy: Jorge L. Arocha , Joaquín Tey
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

tight hypergraphs; triple systems

Kategorie tematyczne

• 05D10: Ramsey theory
• 05B07: Triple systems
• 05C65: Hypergraphs

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2003
• Tom: 23
• Numer: 1
• Strony: 177-187

Daty

wydano

2003

otrzymano

2001-11-26

poprawiono

2002-05-06

Twórcy

autor

Jorge L. Arocha

• Instituto de Matemáticas, UNAM, Ciudad Universitaria, Circuito exterior, México 04510

autor

Joaquín Tey

• Departamento de Matemáticas, UAM-Iztapalapa, Ave. Sn. Rafael Atlixco #186, Col. Vicentina, México 09340

Bibliografia

• [1] J.L. Arocha, J. Bracho and V. Neumann-Lara, On the minimum size of tight hypergraphs, J. Graph Theory 16 (1992) 319-326, doi: 10.1002/jgt.3190160405.
• [2] J.L. Arocha and J. Tey, The size of minimum 3-trees: Cases 3 and 4 mod 6, J. Graph Theory 30 (1999) 157-166, doi: 10.1002/(SICI)1097-0118(199903)30:3<157::AID-JGT1>3.0.CO;2-S
• [3] J.L. Arocha and J. Tey, The size of minimum 3-trees: Case 2 mod 3, Bol. Soc. Mat. Mexicana (3) 8 no. 1 (2002) 1-4.
• [4] L. Lovász, Topological and algebraic methods in graph theory, in: Graph Theory and Related Topics, Proceedings of Conference in Honour of W.T. Tutte, Waterloo, Ontario 1977, (Academic Press, New York, 1979) 1-14.

Identyfikatory

DOI

10.7151/dmgt.1194