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We show that two results on covering of edge colored graphs by monochromatic connected parts can be extended to partitioning. We prove that for any 2-edge-colored non-trivial r-uniform hypergraph H, the vertex set can be partitioned into at most α(H) − r + 2 monochromatic connected parts, where α(H) is the maximum size of a set of vertices that does not(More)
Körner and Malvenuto asked whether one can find`n n/2 ´ linear orderings (i. e., permutations) of the first n natural numbers such that any pair of them place two consecutive integers somewhere in the same position. This led to the notion of graph-different permutations. We extend this concept to directed graphs, focussing on orientations of the(More)
The paper outlines the European and local situation regarding the use of virtual learning environments in technical teacher training and retraining and presents an overview of the content and methods of the continuing education for technical teachers. Introducing and running retraining courses on virtual learning environments including IT and its multimedia(More)
Assume that D is a digraph without cyclic triangles and its vertices are partitioned into classes A 1 ,. .. , A t of independent vertices. A set U = ∪ i∈S A i is called a dominating set of size |S| if for any vertex v ∈ ∪ i / ∈S A i there is a w ∈ U such that (w, v) ∈ E(D). Let β(D) be the cardinality of the largest independent set of D whose vertices are(More)
P-glycoprotein (Pgp) extrudes a large variety of chemotherapeutic drugs from the cells, causing multidrug resistance (MDR). The UIC2 monoclonal antibody recognizes human Pgp and inhibits its drug transport activity. However, this inhibition is partial, since UIC2 binds only to 10-40% of cell surface Pgps, while the rest becomes accessible to this antibody(More)
Lesch-Nyhan syndrome (LNS) is a chronic, progressive neurodevelopmental disorder causing motor and behavioral dysfunction due to decreased synthesis of the enzyme hypoxantine-guanine phosphoribosyltransferase (HPRT). Affected boys have mental retardation, delayed development, extrapyramidal motor disturbances and self-injuring behavior. As hematopoietic(More)
The independence ratio i(G) of a graph G is the ratio of its independence number and the number of vertices. The ultimate categorical independence ratio of a graph G is defined as lim k→∞ i(G ×k), where G ×k denotes the kth categorical power of G. This parameter was introduced by Brown, Nowakowski and Rall, who asked about its value for complete(More)
—We investigate a communication setup where a source output is sent through a free noisy channel first and an additional codeword is sent through a noiseless but expensive channel later. With the help of the second message the decoder should be able to decide with zero-error whether its decoding of the first message was error-free. This scenario leads to(More)
For r ≥ 2, α ≥ r − 1 and k ≥ 1, let c(r, α, k) be the smallest integer c such that the vertex set of any non-trivial r-uniform k-edge-colored hypergraph H with α(H) = α can be covered by c monochromatic connected components. Here α(H) is the maximum cardinality of a subset A of vertices in H such that A does not contain any edges. An old conjecture of Ryser(More)