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Recently in several papers, graphs with maximum neighborhood orderings were characterized and turned out to be algorithmically useful. This paper gives a unified framework for characterizations of those graphs in terms of neighborhood and clique hypergraphs which have the Helly property and whose line graph is chordal. These graphs are dual (in the sense of… (More)

We investigate the coloring properties of mixed interval hypergraphs having two families of subsets: the edges and the co-edges. In every edge at least two vertices have different colors. The notion of a co-edge was introduced recently in [2,3]: in every such a subset at least two vertices have the same color. The upper (lower) chromatic number is defined… (More)

A mixed hypergraph consists of two families of edges: the C-edges and D-edges. In a coloring every C-edge has at least two vertices of the same color, while every D-edge has at least two vertices colored differently. The largest and smallest possible numbers of colors in a coloring are termed the upper and lower chromatic number, ¯ χ and χ, respectively. A… (More)

A mixed hypergraph is a triple H = (X, C, D), where X is the vertex set, and each of C, D is a list of subsets of X. A strict k-coloring of H is a surjection c : X → {1,. .. , k} such that each member of C has two vertices assigned a common value and each member of D has two vertices assigned distinct values. The feasible set of H is {k : H has a strict… (More)

A mixed hypergraph H = (X; A; E) consists of the vertex set X and two families of subsets: the family E of edges and the family A of co-edges. In a coloring every edge E 2 E has at least two vertices of diierent colors, while every co-edge A 2 A has at least two vertices of the same color. The largest (smallest) number of colors for which there exists a… (More)

A mixed hypergraph is a triple H = (V, C, D) where V is the vertex set and C and D are families of subsets of V , the C-edges and D-edges, respectively. A k-colouring of H is a mapping c : V → [k] such that each C-edge has at least two vertices with a Common colour and each D-edge has at least two vertices of Different colours. H is called a planar mixed… (More)

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… (More)