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  • 1
    Electronic Resource
    Electronic Resource
    On representing sylvester-gallai designs (1989)
    Springer
    Discrete & computational geometry 4 (1989), S. 345-348 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A misstated conjecture in [3] leads to an interesting “(1, 3) representation” of the 7-point projective plane inR 4 where points are represented by lines and planes by 3-spaces. The corrected form of the original conjecture will be negated if there is a (1, 3) representation of the 13-point projective plane inR 4 but that matter is not settled.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02187735
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  • 2
    Electronic Resource
    Electronic Resource
    Computing the volume is difficult (1987)
    Springer
    Discrete & computational geometry 2 (1987), S. 319-326 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract For every polynomial time algorithm which gives an upper bound $$\overline {vol}$$ (K) and a lower boundvol(K) for the volume of a convex setK⊂R d , the ratio $$\overline {vol}$$ (K)/vol(K) is at least (cd/logd) d for some convex setK⊂R d .
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02187886
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  • 3
    Electronic Resource
    Electronic Resource
    A Turanlike Neighborhood Condition and Cliques in Graphs (1989)
    Oxford, UK : Blackwell Publishing Ltd
    Annals of the New York Academy of Sciences 555 (1989), S. 0 
    Details
    ISSN: 1749-6632
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Natural Sciences in General
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1749-6632.1989.tb22430.x
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  • 4
    Electronic Resource
    Electronic Resource
    On a Turán type problem of Erdös (1991)
    Springer
    Combinatorica 11 (1991), S. 75-79 
    Details
    ISSN: 1439-6912
    Keywords: 05 C 35 ; 05 C 65
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let L k be the graph formed by the lowest three levels of the Boolean lattice B k , i.e.,V(L k )={0, 1,...,k, 12, 13,..., (k−1)k} and 0is connected toi for all 1≤i≤k, andij is connected toi andj (1≤i〈j≤k). It is proved that if a graph G overn vertices has at leastk 3/2 n 3/2 edges, then it contains a copy of L k .
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01375476
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  • 5
    Electronic Resource
    Electronic Resource
    The prison yard problem (1994)
    Springer
    Combinatorica 14 (1994), S. 287-300 
    Details
    ISSN: 1439-6912
    Keywords: 52 A 30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Given a polygon II withn vertices whose sides arewalls. Guards, located at vertices can see all directions, but cannot see beyond walls. We prove that at most [n/2] guards suffice to see everywhere the whole plane. If II is not convex, then [n/2] suffice.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01212977
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  • 6
    Electronic Resource
    Electronic Resource
    Difference sets and inverting the difference operator (1996)
    Springer
    Combinatorica 16 (1996), S. 87-106 
    Details
    ISSN: 1439-6912
    Keywords: 11 B 05 ; 05 C 65
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For a setA of non-negative numbers, letD(A) (the difference set ofA) be the set of nonnegative differences of elements ofA, and letD k be thek-fold iteration ofD. We show that for everyk, almost every set of non-negative integers containing 0 arises asD k (A) for someA. We also give sufficient conditions for a setA to be the unique setX such that 0∈X andD k (X)=D k (A). We show that for eachm there is a setA such thatD(X)=D(A) has exactly 2 m solutionsX with 0∈X.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01300128
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  • 7
    Electronic Resource
    Electronic Resource
    Decomposition of a convex region by lines (1991)
    Springer
    Archiv der Mathematik 56 (1991), S. 300-312 
    Details
    ISSN: 1420-8938
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01190219
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  • 8
    Electronic Resource
    Electronic Resource
    The second and the third smallest distances on the sphere (1993)
    Springer
    Journal of geometry 46 (1993), S. 55-65 
    Details
    ISSN: 1420-8997
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let s1 (n) denote the largest possible minimal distance amongn distinct points on the unit sphere $$\mathbb{S}^2$$ . In general, let sk(n) denote the supremum of thek-th minimal distance. In this paper we prove and disprove the following conjecture of A. Bezdek and K. Bezdek: s2(n) = s1([n/3]). This equality holds forn 〉 n0 however s2(12) 〉 s1(4). We set up a conjecture for sk(n), that one can always reduce the problem of thek-th minimum distance to the function s1. We prove this conjecture in the casek=3 as well, obtaining that s3(n) = s1([n/5]) for sufficiently largen. The optimal construction for the largest second distance is obtained from a point set of size [n/3] with the largest possible minimal distance by replacing each point by three vertices of an equilateral triangle of the same size ɛ. If ɛ → 0, then s2 tends to s1([n/3]). In the case of the third minimal distance, we start with a point set of size [n/5] and replace each point by a regular pentagon.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01231000
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  • 9
    Electronic Resource
    Electronic Resource
    On the shape of the convex hull of random points (1988)
    Springer
    Probability theory and related fields 77 (1988), S. 231-240 
    Details
    ISSN: 1432-2064
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Denote by E n the convex hull of n points chosen uniformly and independently from the d-dimensional ball. Let Prob(d, n) denote the probability that E n has exactly n vertices. It is proved here that Prob(d, 2 d/2 d -ɛ)→1 and Prob(d, 2 d/2 d (3/4)+ɛ)→0 for every fixed ɛ〉0 when d→∞. The question whether E n is a k-neighbourly polytope is also investigated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00334039
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  • 10
    Electronic Resource
    Electronic Resource
    Graphs of diameter 3 with the minimum number of edges (1990)
    Springer
    Graphs and combinatorics 6 (1990), S. 333-337 
    Details
    ISSN: 1435-5914
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The graphG is called a porcupine, ifG∣A is a complete graph for some setA, every other vertex has degree one, and its only edge is joined toA. In this paper a conjecture of Bollobás is settled almost completely. Namely, it is proved that ifG is a graph onn vertices of diameter 3 with maximum degreeD, D 〉 2.31 $$\sqrt n $$ ,D ≠ (n − 1)/2 and it has the mimimum number of edges, then it is a porcupine.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01787701
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