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  • 1
    Digitale Medien
    Digitale Medien
    On Conway's Thrackle Conjecture (1997)
    Springer
    Discrete & computational geometry 18 (1997), S. 369-376 
    Details
    ISSN: 1432-0444
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract. A thrackle is a graph drawn in the plane so that its edges are represented by Jordan arcs and any two distinct arcs either meet at exactly one common vertex or cross at exactly one point interior to both arcs. About 40 years ago, J. H. Conway conjectured that the number of edges of a thrackle cannot exceed the number of its vertices. We show that a thrackle has at most twice as many edges as vertices. Some related problems and generalizations are also considered.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/PL00009322
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  • 2
    Digitale Medien
    Digitale Medien
    On the graph of large distances (1989)
    Springer
    Discrete & computational geometry 4 (1989), S. 541-549 
    Details
    ISSN: 1432-0444
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract For a setS of points in the plane, letd 1〉d 2〉... denote the different distances determined byS. Consider the graphG(S, k) whose vertices are the elements ofS, and two are joined by an edge iff their distance is at leastd k . It is proved that the chromatic number ofG(S, k) is at most 7 if |S|≥constk 2. IfS consists of the vertices of a convex polygon and |S|≥constk 2, then the chromatic number ofG(S, k) is at most 3. Both bounds are best possible. IfS consists of the vertices of a convex polygon thenG(S, k) has a vertex of degree at most 3k − 1. This implies that in this case the chromatic number ofG(S, k) is at most 3k. The best bound here is probably 2k+1, which is tight for the regular (2k+1)-gon.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02187746
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  • 3
    Digitale Medien
    Digitale Medien
    Factoring polynomials with rational coefficients (1982)
    Springer
    Mathematische Annalen 261 (1982), S. 515-534 
    Details
    ISSN: 1432-1807
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01457454
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  • 4
    Digitale Medien
    Digitale Medien
    Entropy splitting for antiblocking corners and perfect graphs (1990)
    Springer
    Combinatorica 10 (1990), S. 27-40 
    Details
    ISSN: 1439-6912
    Schlagwort(e): 05C15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02122693
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  • 5
    Digitale Medien
    Digitale Medien
    On the number of halving planes (1990)
    Springer
    Combinatorica 10 (1990), S. 175-183 
    Details
    ISSN: 1439-6912
    Schlagwort(e): 52 A 37
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02123008
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  • 6
    Digitale Medien
    Digitale Medien
    Rubber bands, convex embeddings and graph connectivity (1988)
    Springer
    Combinatorica 8 (1988), S. 91-102 
    Details
    ISSN: 1439-6912
    Schlagwort(e): 05 C 40 ; 52 A 20
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract We give various characterizations ofk-vertex connected graphs by geometric, algebraic, and “physical” properties. As an example, a graphG isk-connected if and only if, specifying anyk vertices ofG, the vertices ofG can be represented by points of ℝk−1 so that nok are on a hyper-plane and each vertex is in the convex hull of its neighbors, except for thek specified vertices. The proof of this theorem appeals to physics. The embedding is found by letting the edges of the graph behave like ideal springs and letting its vertices settle in equilibrium. As an algorithmic application of our results we give probabilistic (Monte-Carlo and Las Vegas) algorithms for computing the connectivity of a graph. Our algorithms are faster than the best known (deterministic) connectivity algorithms for allk≧√n, and for very dense graphs the Monte Carlo algorithm is faster by a linear factor.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02122557
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  • 7
    Digitale Medien
    Digitale Medien
    On finite Dirichlet series (1971)
    Springer
    Acta mathematica hungarica 22 (1971), S. 227-231 
    Details
    ISSN: 1588-2632
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01896014
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  • 8
    Digitale Medien
    Digitale Medien
    On the sum of matroids (1973)
    Springer
    Acta mathematica hungarica 24 (1973), S. 329-333 
    Details
    ISSN: 1588-2632
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01958043
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  • 9
    Digitale Medien
    Digitale Medien
    Applications of product colouring (1974)
    Springer
    Acta mathematica hungarica 25 (1974), S. 335-340 
    Details
    ISSN: 1588-2632
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01886093
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  • 10
    Digitale Medien
    Digitale Medien
    On some connectivity properties of Eulerian graphs (1976)
    Springer
    Acta mathematica hungarica 28 (1976), S. 129-138 
    Details
    ISSN: 1588-2632
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01902503
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