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  • 1990-1994  (2)
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  • 1
    Electronic Resource
    Electronic Resource
    Entropy splitting for antiblocking corners and perfect graphs (1990)
    Springer
    Combinatorica 10 (1990), S. 27-40 
    Details
    ISSN: 1439-6912
    Keywords: 05C15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We characterize pairs of convex setsA, B in thek-dimensional space with the property that every probability distribution (p 1,...,p k ) has a repsesentationp i =a l .b i , a∃A, b∃B. Minimal pairs with this property are antiblocking pairs of convex corners. This result is closely related to a new entropy concept. The main application is an information theoretic characterization of perfect graphs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02122693
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    On the number of halving planes (1990)
    Springer
    Combinatorica 10 (1990), S. 175-183 
    Details
    ISSN: 1439-6912
    Keywords: 52 A 37
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract LetS ⊂ℝ3 be ann-set in general position. A plane containing three of the points is called a halving plane if it dissectsS into two parts of equal cardinality. It is proved that the number of halving planes is at mostO(n 2.998). As a main tool, for every setY ofn points in the plane a setN of sizeO(n 4) is constructed such that the points ofN are distributed almost evenly in the triangles determined byY.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02123008
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    Paper (German National Licenses)
    Fulltext
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