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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)

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)

—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)

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 the… (More)

- Krisztián Kállay, Zoltán Liptai, Gábor Benyó, Csaba Kassa, Veronika Goda, János Sinkó +2 others
- Metabolic Brain Disease
- 2012

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)

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)