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- Paul Erdös, Zoltán Füredi, András Hajnal, Péter Komjáth, Vojtech Rödl, Ákos Seress
- Discrete Mathematics
- 1986

Assume that a graph G has a good-coloring which uses at most r colors in the neighborhood of every vertex. We call this kind of coloring a local r-coloring . Is it true that the chromatic number of G is bounded? For r = 1 the answer is easy, G is bipartite, as it cannot have an odd circuit . For r = 2, however, the situation is completely different. A graph… (More)

- Ákos Seress
- 1999

If a black box simple group is known to be isomorphic to a classical group over a field of known characteristic, a Las Vegas algorithm is used to produce an explicit isomorphism. This is used to upgrade all nearly linear time Monte Carlo permutation group algorithms to Las Vegas algorithms when the input group has no composition factor isomorphic to an… (More)

- László Babai, Eugene M. Luks, Ákos Seress
- FOCS
- 1988

We present new algorithms for permutation group manipulation. Our methods result in an improvement of nearly an order of magnitude in the worst-case analysis for the fundamental problems of finding strong generating sets and testing membership. The normal structure of the group is brought into play even for such elementary issues. An essential element is… (More)

- László Babai, Ákos Seress
- J. Comb. Theory, Ser. A
- 1988

In this paper we are concerned with the conjecture that, for any set of generators S of the symmetric group Sym(n), the word length in terms of S of every permutation is bounded above by a polynomial of n. We prove this conjecture for sets of generators containing a permutation fixing at least 37% of the points.

- László Babai, Eugene M. Luks, Ákos Seress
- STOC
- 1987

We show that the basic problems of permutation group manipulation admit efficient parallel solutions. Given a permutation group G by a list of generators, we find a set of NC-efficient strong generators in NC. Using this, we show, that the following problems are in NC: membership in G; determining the order of G; finding the center of G; finding a… (More)

- László Babai, Gene Cooperman, Larry Finkelstein, Ákos Seress
- ISSAC
- 1991

A base of a permutation group G is a subset B of the permutation domain such that only the identity of G fixes B pointwise. The permutation representations of important classes of groups, including all finite simple groups other than the alternating groups, admit O(log n) size bases, where n is the size of the permutation domain. Groups with very small… (More)

Let w be a non-trivial word in two variables. We prove that the probability that two randomly chosen elements x, y of a nonabelian finite simple group S satisfy w(x, y) = 1 tends to 0 as |S| → ∞. As a consequence, we obtain a new short proof of a well-known conjecture of Magnus concerning free groups, as well as some applications to profinite groups.… (More)

- László Babai, Eugene M. Luks, Ákos Seress
- SIAM J. Comput.
- 1997

We present new algorithms for permutation group manipulation. Our methods result in an improvement of nearly an order of magnitude in the worst-case analysis for the fundamental problems of finding strong generating sets and testing membership. The normal structure of the group is brought into play even for such elementary issues. An essential element is… (More)

- László Lovász, Ákos Seress
- Eur. J. Comb.
- 1993

We study the lattice (grid) generated by the incidence vectors of cocycles of a binary matroid and its dual lattice. We characterize those binary matroids for which the obvious necessary conditions for a vector to belong to the cocycle lattice are also sufficient. This characterization yields a polynomial time algorithm to check whether a matroid has this… (More)

- Péter L. Erdös, Ákos Seress, László A. Székely
- Combinatorica
- 2000

We prove Erdős-Ko-Rado and Hilton-Milner type theorems for t-intersecting k-chains in posets using the kernel method. These results are common generalizations of the original EKR and HM theorems, and our earlier results for intersecting k-chains in the Boolean algebra. For intersecting k-chains in the c-truncated Boolean algebra we also prove an exact EKR… (More)