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The size of minimum 3-trees: Cases 3 and 4 mod 6

✍ Scribed by Arocha, Jorge L.; Tey, Joaqu�n

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
177 KB
Volume
30
Category
Article
ISSN
0364-9024

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✦ Synopsis

A 3-uniform hypergraph is called a minimum 3-tree, if for any 3coloring of its vertex set there is a heterochromatic edge and the hypergraph has the minimum possible number of edges. Here we show that the number of edges in such 3-tree is

for any number of vertices n ≡ 3, 4 (mod 6).

📜 SIMILAR VOLUMES

The size of minimum 3-trees
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✍ Jorge L. Arocha; Joaquín Tey 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 199 KB

## Abstract A 3‐uniform hypergraph (3‐graph) is said to be tight, if for any 3‐partition of its vertex set there is a transversal triple. We give the final steps in the proof of the conjecture that the minimum number of triples in a tight 3‐graph on __n__ vertices is exactly $\left\lceil n(n-2)/3 \

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