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Currently displaying 1 – 6 of 6

Order by Relevance | Title | Year of publication

The arc-width of a graph.

Barát, János; Hajnal, Péter — 2001

The Electronic Journal of Combinatorics [electronic only]

On winning fast in Avoider-Enforcer games.

Barát, János; Stojaković, Miloš — 2010

The Electronic Journal of Combinatorics [electronic only]

Towards the Albertson conjecture.

Barát, János; Tóth, Géza — 2010

The Electronic Journal of Combinatorics [electronic only]

Notes on nonrepetitive graph colouring.

Barát, János; Wood, David R. — 2008

The Electronic Journal of Combinatorics [electronic only]

Bounded-degree graphs have arbitrarily large geometric thickness.

Barát, János; Matoušek, Jirí; Wood, David R. — 2006

The Electronic Journal of Combinatorics [electronic only]

A contribution to infinite disjoint covering systems

János Barát; Péter P. Varjú — 2005

Journal de Théorie des Nombres de Bordeaux

Let the collection of arithmetic sequences ${d_{i} n + b_{i} : n \in ℤ}_{i \in I}$ be a disjoint covering system of the integers. We prove that if $d_{i} = p^{k} q^{l}$ for some primes $p, q$ and integers $k, l \geq 0$ , then there is a $j \neq i$ such that $d_{i} | d_{j}$ . We conjecture that the divisibility result holds for all moduli. A disjoint covering system is called saturated if the sum of the reciprocals of the moduli is equal to $1$ . The above conjecture holds for saturated systems with $d_{i}$ such that the product of its prime factors is at most $1254$ .

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