A mixed hypergraph is a triple 𝓗 = (X,𝓒,𝓓) where X is the vertex set and each of 𝓒, 𝓓 is a family of subsets of X, the 𝓒-edges and 𝓓-edges, respectively. A k-coloring of 𝓗 is a mapping c: X → [k] such that each 𝓒-edge has two vertices with the same color and each 𝓓-edge has two vertices with distinct colors. 𝓗 = (X,𝓒,𝓓) is called a mixed hypertree if there exists a tree T = (X,𝓔) such that every 𝓓-edge and every 𝓒-edge induces a subtree of T. A mixed hypergraph 𝓗 is called uniquely colorable if it has precisely one coloring apart from permutations of colors. We give the characterization of uniquely colorable mixed hypertrees.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1108,
author = {Angela Niculitsa and Vitaly Voloshin},
title = {About uniquely colorable mixed hypertrees},
journal = {Discussiones Mathematicae Graph Theory},
volume = {20},
year = {2000},
pages = {81-91},
zbl = {0992.05038},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1108}
}
Angela Niculitsa; Vitaly Voloshin. About uniquely colorable mixed hypertrees. Discussiones Mathematicae Graph Theory, Tome 20 (2000) pp. 81-91. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1108/
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