Vitaly I. Voloshin

Learn More
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 introduce the notion of a co-edge of a hypergraph, which is a subset of vertices to be colored so that at least two vertices are of the same color. Hypergraphs with both edges and co-edges are called mixed hypergraphs. The maximal number of colors for which there exists a mixed hypergraph coloring using all the colors is called the upper chromatic number(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)
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)
We introduce the notion of an anti-edge of a hypergraph, which is a non-overall polychromatic subset of vertices. The maximal number of colors, for which there exists a coloring of a hy-pergraph using all colors, is called an upper chromatic number of a hypergraph H and denoted by ¯ χ(H). The general algorithm for computing the numbers of all colorings of(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)