منابع مشابه
About uniquely colorable mixed hypertrees
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 ...
متن کاملNote about the upper chromatic number of mixed hypertrees
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 proper k-coloring of H is a mapping c : X → [k] such that each C-edge has two vertices with a common color and each D-edge has two vertices with distinct colors. Upper chromatic number is the maximum number of colors that can be used in a ...
متن کاملGeombinatorial Mixed Hypergraph Coloring Problems
Can you color Rn so that point sets of one sort are never monochromatic, while point sets of another sort always are? If so, how many colors did you use, and can you do the job with more or fewer colors?
متن کاملMaximum Likelihood Markov Hypertrees
One popular class of such models are Markov networks, which use an undirected graph to represent dependencies among variables. Markov networks of low tree-width (i.e. having a triangulation with small cliques ) allow efficient computations, and are useful as learned probability models [8]. A well studied case is that in which the dependency structure is known in advance. In this case the underl...
متن کاملNoncrossing Hypertrees
Hypertrees and noncrossing trees are well-established objects in the combinatorics literature, but the hybrid notion of a noncrossing hypertree has received less attention. In this article I investigate the poset of noncrossing hypertrees as an induced subposet of the hypertree poset. Its dual is the face poset of a simplicial complex, one that can be identified with a generalized cluster compl...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2006
ISSN: 0166-218X
DOI: 10.1016/j.dam.2005.05.019