Vitaly I. Voloshin

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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)
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 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)