# János Komlós

• Combinatorica
• 1981
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)
• STOC
• 1983
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)
• Combinatorica
• 1997
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)
• STOC
• 1987
In this paper we show that a wide class of probabilistic algorithms can be simulated by deterministic algorithms. Namely if there is a test in LOGSPACE so that a random sequence of length (log <italic>n</italic>)<supscrpt>2</supscrpt> / log log <italic>n</italic> passes the test with probability at least 1/<italic>n</italic> then a deterministic sequence(More)
• Discrete Mathematics
• 2001
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)