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

Improving a result of Erdős, Gyárfás and Pyber for large n we show that for every integer r 2 there exists a constant n0 = n0(r) such that if n n0 and the edges of the complete graph Kn are colored with r colors then the vertex set of Kn can be partitioned into at most 100r log r vertex disjoint monochromatic cycles. © 2006 Elsevier Inc. All rights reserved.

- 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. ∗2000 Mathematics Subject Classification: 05C55, 05C38. The second author was supported in part by OTKA Grants T038198 and T046234.

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

Let fd(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 > n0(D) vertices, f2(G) = n − D − 1 and f3(G) ≥ n − O(D). For d ≥ 4, fd(G) depends strongly on the actual structure of G, not only on the maximum degree of G. We prove… (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)

- 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.

- 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)

- Aart Blokhuis, Ralph J. Faudree, András Gyárfás, Miklós Ruszinkó
- J. Comb. Theory, Ser. B
- 2001

(joint work with Aart Blokhuis, András Gyárfás and Miklós Ruszinkó) For positive integers k ≤ n and t let χ t (k, n) denote the minimum number of colors such that at least in one of the total t colorings of edges of K n all k 2 edges of every K k ⊆ K n get different colors. Generalizing a result of Körner and Simonyi, it is shown in this paper that χ t (3,… (More)

- András Gyárfás, Miklós Ruszinkó, Gábor N. Sárközy, Endre Szemerédi
- Electr. J. Comb.
- 2011

We show in this paper that in every 3-coloring of the edges of K all but o(n) of its vertices can be partitioned into three monochromatic cycles. From this, using our earlier results, actually it follows that we can partition all the vertices into at most 17 monochromatic cycles, improving the best known bounds. If the colors of the three monochromatic… (More)

- Alan M. Frieze, Ryan R. Martin, Julien Moncel, Miklós Ruszinkó, Clifford D. Smyth
- Discrete Mathematics
- 2007

In this paper we deal with codes identifying sets of vertices in random networks; that is, (1,≤ 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 (1,≤ 1)-identifying codes are of special interest. For random… (More)

- Miklós Ruszinkó, Peter Vanroose
- IEEE Trans. Information Theory
- 1997