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  • 1
    Electronic Resource
    Electronic Resource
    Bounds for arrays of dots with distinct slopes or lengths (1992)
    Springer
    Combinatorica 12 (1992), S. 39-44 
    Details
    ISSN: 1439-6912
    Keywords: 05 C
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Ann×m sonar sequence is a subset of then×m grid with exactly one point in each column, such that the $$\mathop 2\limits^m $$ vectors determined by them are all distinct. We show that for fixedn the maximalm for which a sonar sequence exists satisfiesn−Cn 11/20〈m〈n+4n 2/3 for alln andm〉n+c logn log logn for infinitely manyn. Another problem concerns the maximal numberD of points that can be selected from then×m grid so that all the $$\mathop 2\limits^D $$ vectors have slopes. We proven 1/2≪D≪n 4/5
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01191203
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  • 2
    Electronic Resource
    Electronic Resource
    Clique coverings of the edges of a random graph (1993)
    Springer
    Combinatorica 13 (1993), S. 1-5 
    Details
    ISSN: 1439-6912
    Keywords: 05 C 80
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The edges of the random graph (with the edge probabilityp=1/2) can be covered usingO(n 2lnlnn/(lnn)2) cliques. Hence this is an upper bound on the intersection number (also called clique cover number) of the random graph. A lower bound, obtained by counting arguments, is (1−ɛ)n 2/(2lgn)2.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01202786
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  • 3
    Electronic Resource
    Electronic Resource
    A variant of the classical Ramsey problem (1997)
    Springer
    Combinatorica 17 (1997), S. 459-467 
    Details
    ISSN: 1439-6912
    Keywords: 05D10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For fixed integersp, q an edge coloring of a complete graphK is called a (p, q)-coloring if the edges of everyK p ⊑K are colored with at leastq distinct colors. Clearly, (p, 2)-colorings are the classical Ramsey colorings without monochromaticK p subgraphs. Letf(n, p, q) be the minimum number of colors needed for a (p, q)-coloring ofK n . We use the Local Lemma to give a general upper bound forf. We determine for everyp the smallestq for whichf(n, p, q) is linear inn and the smallestq for whichf(n, p, q) is quadratic inn. We show that certain special cases of the problem closely relate to Turán type hypergraph problems introduced by Brown, Erdős and T. Sós. Other cases lead to problems concerning proper edge colorings of complete graphs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01195000
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  • 4
    Electronic Resource
    Electronic Resource
    How to decrease the diameter of triangle-free graphs (1998)
    Springer
    Combinatorica 18 (1998), S. 493-501 
    Details
    ISSN: 1439-6912
    Keywords: AMS Subject Classification (1991) Classes:  05C12, 05C35
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Assume that G is a triangle-free graph. Let be the minimum number of edges one has to add to G to get a graph of diameter at most d which is still triangle-free. It is shown that for connected graphs of order n and of fixed maximum degree. The proof is based on relations of and the clique-cover number of edges of graphs. It is also shown that the maximum value of over (triangle-free) graphs of order n is . The behavior of is different, its maximum value is . We could not decide whether for connected (triangle-free) graphs of order n with a positive ε.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004930050035
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  • 5
    Electronic Resource
    Electronic Resource
    Kleine Schwingungen dynamischer Systeme (1953)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 4 (1953), S. 215-219 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Summary The Hamiltonian differential equations for small displacements of a dynamical system with a finite number of degrees of freedom are solved by use of the methods of linear algebra. In this way the stability of the equilibrium configuration or uniform motion in the case of positive definite total energy is demonstrated. Especially gyroscopic terms may appear in the hamiltonian, making impossible the usual proof of stability by means of transformation to normal coordinates. This method is then applied to the Weierstrass procedure of solution. For use in the above integration, the spectral representation of a matrix with linear elementary divisors is given through the adjoint of its characteristic matrix.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02083517
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  • 6
    Electronic Resource
    Electronic Resource
    Osculation vertices in arrangements of curves (1973)
    Springer
    Geometriae dedicata 1 (1973), S. 322-333 
    Details
    ISSN: 1572-9168
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00147765
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  • 7
    Book
    Book
    ¬The¬ probabilistic method (1992)
    New York u.a. :Wiley,
    Details
    Title: ¬The¬ probabilistic method
    Author: Alon, Noga
    Contributer: Spencer, Joel H. , Erdos, Paul
    Publisher: New York u.a. :Wiley,
    Year of publication: 1992
    Pages: 254 S.
    Type of Medium: Book
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    Zuse Institute Berlin get availability status
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