Ákos Seress

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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)
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)
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)
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)
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)
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)
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)