The theory of mixed hypergraph coloring was first introduced by Voloshin in 1993 and has been growing ever since. The proper coloring of a mixed hypergraph H = (X, C,D) is the coloring of the vertex set X so that no D-hyperedge is monochromatic and no C-hyperedge is polychromatic. A mixed hypergraph with hyperedges of type D, C or B is commonly known as a D, C, or B-hypergraph respectively wher...

Claude BERGE C.N.R.S., Paris The hypergraphs whose chromatic number is ~ 2 ("bicolorable" hypergraphs) were introduced by E.W. Miller [13] under the name of "set-systems with Property B". This concept appears in Number Theory (see [5], [10]). It is also useful for some problems in positional games and Operations Research (see [3], [4], [7]); different results have been found under the form of i...

Let Cn denote the 3-uniform hypergraph loose cycle, that is the hypergraph with vertices v1, . . . , vn and edges v1v2v3, v3v4v5, v5v6v7, . . . , vn−1vnv1. We prove that every red-blue colouring of the edges of the complete 3-uniform hypergraph with N vertices contains a monochromatic copy of Cn, where N is asymptotically equal to 5n/4. Moreover this result is (asymptotically) best possible.

HYPERGRAPH MODELS FOR SPARSE MATRIX PARTITIONING AND REORDERING  Umit V. C ataly urek Ph.D. in Computer Engineering and Information Science Supervisor: Assoc. Prof. Cevdet Aykanat November, 1999 Graphs have been widely used to represent sparse matrices for various scienti c applications including one-dimensional (1D) decomposition of sparse matrices for parallel sparse-matrix vector multiplic...

An r-uniform hypergraph is k-edge-hamiltonian iff it still contains a hamiltonian-chain after deleting any k edges of the hypergraph. What is the minimum number of edges in such a hypergraph? We give lower and upper bounds for this question for several values of r and k. © 2007 Elsevier B.V. All rights reserved.

For a fixed 3-uniform hypergraph F , call a hypergraph F-free if it contains no subhypergraph isomorphic to F . Let ex(n,F) denote the size of a largest F-free hypergraph G ⊆ [n]. Let Fn(F) denote the number of distinct labelled F-free G ⊆ [n]. We show that Fn(F) = 2ex(n,F)+o(n 3), and discuss related problems.

In this paper, we introduce contextual hypergraph grammars, which generalize the total contextual string grammars. We study the position of the class of languages generated by contextual hypergraph grammars in comparison with graph languages generated by hyperedge replacement grammars and double-pushout hypergraph grammars. Moreover, several examples show the potential of the new class of gramm...

This article explores possibilities of partitioning the vertex set of a given simple loop-free Sperner hypergraph into a union of transversals. Studies are done on the possible number of transversals in such partitions, followed by forming a hypergraph (on the vertex set of the given hypergraph) that consists of transversals for hyperedges. AMS Subject Classification: 05C65

Some results on matchings in a hypergraph cut vertex, cut edge of hypergraph have been obtained analogous to the results in a simple graph. In this paper we have obtained some interesting properties of a hypergraph. The notations and terminology that are used in this paper are the same as in [1].