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- András Gyárfás, Miklós Ruszinkó, Gábor N. Sárközy, Endre Szemerédi
- Combinatorica
- 2007

We prove – for sufficiently large n – the following conjecture of Faudree and Schelp: R(Pn, Pn, Pn) = 2n − 1 for odd n, 2n − 2 for even n, for the three-color Ramsey numbers of paths on n vertices.

- Miklós Ruszinkó
- J. Comb. Theory, Ser. A
- 1994

Let T(r; n) denote the maximum number of subsets of an n-set satisfying the condition in the title. It is proved in a purely combinatorial way, that for n suuciently large log 2 T(r; n) n 8 log 2 r r 2 holds.

- András Gyárfás, Miklós Ruszinkó, Gábor N. Sárközy, Endre Szemerédi
- J. Comb. Theory, Ser. B
- 2006

Improving a result of Erd˝ os, Gyárfás and Pyber for large n we show that for every integer r 2 there exists a constant n 0 = n 0 (r) such that if n n 0 and the edges of the complete graph K n are colored with r colors then the vertex set of K n can be partitioned into at most 100r log r vertex disjoint monochromatic cycles.

- Noga Alon, András Gyárfás, Miklós Ruszinkó
- Journal of Graph Theory
- 2000

Let f d (G) denote the minimum number of edges that have to be added to a graph G to transform it into a graph of diameter at most d. We prove that for any graph G with maximum degree D and n > n 0 (D) vertices, f 2 (G) = n − D − 1 and f 3 (G) ≥ n − O(D 3). For d ≥ 4, f d (G) depends strongly on the actual structure of G, not only on the maximum degree of… (More)

- Miklós Csürös, Miklós Ruszinkó
- IEEE Transactions on Information Theory
- 2005

The zero-error capacity region of r-out-of-T user multiple-access OR channel is investigated. A family F of subsets of [n] = {1, ..., n} is an r-single-user-tracing superimposed code (r-SUT) if there exists such a single-user-tracing function /spl phi/:2/sup [n]/ /spl rarr/ F that for all F' /spl sube/ F with 1 /spl les/ |F'| /spl les/ r, /spl phi/(/spl… (More)

- Zoltán Füredi, Miklós Ruszinkó
- IEEE Trans. Information Theory
- 1999

A family of n-dimensional unit norm vectors is a Euclidean superimposed code, if the sums of any two distinct at most m-tuples of vectors are separated by a certain minimum Euclidean distance d. Ericson and Györfi [8] proved that the rate of such a code is between (log m)/4m and (log m)/m for m large enough. In this paper – improving the above longstanding… (More)

- A. Frieze, R. Martin, J. Moncel, M. Ruszinko, C. Smyth
- Proceedings. International Symposium on…
- 2005

In this paper we deal with codes identifying sets of vertices in random graphs, that is l-identifying codes. These codes enable us to detect sets of faulty processors in a multiprocessor system, assuming that the maximum number of faulty processors is bounded by a fixed constant l. The l-identifying codes or simply identifying codes are of special interest.… (More)

- Tom Bohman, Alan M. Frieze, Ryan R. Martin, Miklós Ruszinkó, Clifford D. Smyth
- Random Struct. Algorithms
- 2007

- Tom Bohman, Colin Cooper, Alan M. Frieze, Ryan R. Martin, Miklós Ruszinkó
- Electr. J. Comb.
- 2003

Let c be a positive constant. We show that if r = cn 1/3 and the members of [n] r are chosen sequentially at random to form an intersecting hypergraph then with limiting probability (1 + c 3) −1 , as n → ∞, the resulting family will be of maximum size n−1 r−1 .

- Tom Bohman, Alan M. Frieze, Miklós Ruszinkó, Lubos Thoma
- Combinatorics, Probability & Computing
- 2001