Miklós Ruszinkó

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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.
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)
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)
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)
(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)
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)
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)