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.