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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1194,
author = {Jorge L. Arocha and Joaqu\'\i n Tey},
title = {The size of minimum 3-trees: cases 0 and 1 mod 12},
journal = {Discussiones Mathematicae Graph Theory},
volume = {23},
year = {2003},
pages = {177-187},
zbl = {1038.05040},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1194}
}
Jorge L. Arocha; Joaquín Tey. The size of minimum 3-trees: cases 0 and 1 mod 12. Discussiones Mathematicae Graph Theory, Tome 23 (2003) pp. 177-187. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1194/
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