# Hanno Lefmann

• J. Algorithms
• 1994
The Regularity Lemma of Szemer edi is a result that asserts that every graph can be partitioned in a certain regular way. This result has numerous applications, but its known proof is not algorithmic. Here we rst demonstrate the computational diiculty of nding a regular partition; we show that deciding if a given partition of an input graph satisses the(More)
• MFCS
• 1995
In this paper typical properties of large random Boolean AND/OR formulas are investigated. Such formulas with n variables are viewed as rooted binary trees chosen from the uniform distribution of all rooted binary trees on m nodes, where n is xed and m tends to innnity. The leaves are labeled by literals and the inner nodes by the connectives AND/OR, both(More)
• Combinatorica
• 1995
In this paper new proofs of the Canonical Ramsey Theorem, which originally has been proved by ErdSs and Rado, are given. These yield improvements over the known bounds for the arising Erd6s-Rado numbers ER(k; l), where the numbers ER(k; l) are defined as the least positive integer n such that for every partition of the k-element subsets of a totally ordered(More)
We consider anti-Ramsey type results. For a given coloring ∆ of the k-element subsets of an n-element set X, where two k-element sets with nonempty intersection are colored differently, let inj∆(k, n) be the largest size of a subset Y ⊆ X, such that the k-element subsets of Y are colored pairwise differently. Taking the minimum over all colorings, i.e.(More)
• Discrete Mathematics
• 1995
For positive integers m and r define f (m, r) to be the minimum integer n such that for every coloring of {1,2 . . . . . n} with r colors, there exist two monochromatic subsets B 1, B2~{1, 2 . . . . . n} (but not necessarily of the same color) which satisfy: (i)IBll=lB21=m; (ii) The largest number in B 1 is smaller than the smallest number in B2; (iii) The(More)
• MFCS
• 1998
We consider the problem of approximating the independence number and the chromatic number of k-uniform hypergraphs on n vertices. For xed integers k 2, we obtain for both problems that one can achieve in polynomial time approximation ratios of at most O(n=(log 1) n)2). This extends results of Boppana and Halld orsson [5] who showed for the graph case that(More)