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- Andrzej Dudek, Alan M. Frieze
- Random Struct. Algorithms
- 2013

In this paper we show that e/n is the sharp threshold for the existence of tight Hamilton cycles in random k-uniform hypergraphs, for all k ≥ 4. When k = 3 we show that 1/n is an asymptotic… (More)

- Andrzej Dudek, Alan M. Frieze, Andrzej Rucinski
- Electr. J. Comb.
- 2012

Let K (k) n be a complete k-uniform hypergraph. A loose Hamilton cycle in K (k) n is a cycle of order n in which every pair of adjacent edges intersects in a single vertex. We color every edge of K… (More)

- Andrzej Dudek, Vojtech Rödl
- Combinatorica
- 2011

Extending the problem of determining Ramsey numbers Erdős and Rogers introduced the following function. For given integers 2 ≤ s < t let fs,t(n) = min {max{|S| : S ⊆ V (H) and H[S] contains no Ks}} ,… (More)

- Andrzej Dudek, Troy Retter, Vojtech Rödl
- J. Comb. Theory, Ser. B
- 2014

Extending the concept of Ramsey numbers, Erdős and Rogers introduced the following function. For given integers 2 ≤ s < t let fs,t(n) = min{max{|W | : W ⊆ V (G) and G[W ] contains no Ks}}, where the… (More)

Regression analysis is perhaps the best known and most widely used method used for the analysis of dependence; that is, for examining the relationship between a set of independent variables (X’s) and… (More)

- Andrzej Dudek, Vojtech Rödl
- Experimental Mathematics
- 2008

Let f(2, 3, 4) denote the smallest integer n such that there exists a K4-free graph of order n for which any 2-coloring of its edges yields at least one monochromatic triangle. It is well-known that… (More)

- Andrzej Dudek, Vojtech Rödl
- J. Comb. Theory, Ser. B
- 2010

The vertex Folkman number F (r, n,m), n < m, is the smallest integer t such that there exists a Km-free graph of order t with the property that every r-coloring of its vertices yields a monochromatic… (More)

- Andrzej Dudek, Dhruv Mubayi
- Journal of Graph Theory
- 2014

The well-known Ramsey number r(t, u) is the smallest integer n such that every Ktfree graph of order n contains an independent set of size u. In other words, it contains a subset of u vertices with… (More)

- Andrzej Dudek, Alan M. Frieze, Charalampos E. Tsourakakis
- SIAM J. Discrete Math.
- 2015

An edge colored graph G is rainbow edge connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection of a connected graph G, denoted by rc(G), is the… (More)

- Andrzej Dudek, Alan M. Frieze, Andrzej Rucinski, Matas Sileikis
- Inf. Process. Lett.
- 2013

In this paper we asymptotically count d-regular k-uniform hypergraphs on n vertices, provided k is fixed and d = d(n) = o(n). In doing so, we extend to hypergraphs a switching technique of McKay and… (More)