János Komlós

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Let A:(at;) be an zxn matrix whose entries for i=j are independent random variables and ai;:aii. Suppose that every a;; is bounded and for eveÍy i>j we have Eaii:!, D2ai,:62 and Eaii-v. E. P. Wigner determined the asymptotic behavior of the eigenvalues of I (semi-circle law). In particular, for any c >2a with probability I o (1) all eigenvalues except for(More)
The purpose of this paper is to describe a sorting network of size 0(n log n) and depth 0(log n). A natural way of sorting is through consecutive halvings: determine the upper and lower halves of the set, proceed similarly within the halves, and so on. Unfortunately, while one can halve a set using only 0(n) comparisons, this cannot be done in less than(More)
The Regularity Lemma [16] is a powerful tool in Graph Theory and its applications. It basically says that every graph can be well approximated by the union of a constant number of random-looking bipartite graphs called regular pairs (see the definitions below). These bipartite graphs share many local properties with random bipartite graphs, e.g. most(More)
In this paper we prove the following conjecture of Alon and Yuster. Let H be a graph with h vertices and chromatic number k. There exist constants c(H) and n0(H) such that if n¿n0(H) and G is a graph with hn vertices and minimum degree at least (1− 1=k)hn+ c(H), then G contains an H -factor. In fact, we show that if H has a k-coloring with color-class sizes(More)