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  • 1
    Electronic Resource
    Electronic Resource
    On the existence of special homogeneous monoids (1974)
    Springer
    Semigroup forum 9 (1974), S. 95-101 
    Details
    ISSN: 1432-2137
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The paper contains constructions of finite transformation monoids such that the number of transformations from one point into another is a constant and whose groups of units are not transitive.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02194838
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Embeddings of graphs in euclidean spaces (1989)
    Springer
    Discrete & computational geometry 4 (1989), S. 349-364 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The dimension of a graphG=(V, E) is the minimum numberd such that there exists a representation $$x \to \bar x \in R^d (x \in V)$$ and a thresholdt such thatxy εE iff $$\mathop x\limits^ - \mathop y\limits^ - \geqslant t$$ . We prove that d(G)≤n−x(G) and $$d(G) \leqslant n - \sqrt n $$ wheren=|V| andx(G) is the chromatic number ofG; we present upper bounds for the dimension of graphs with a large girth and we show that the complement of a forest can be represented by unit vectors inR 6. We prove that d(G)≥1/15n for most graphs and that there are 3-regular graphs with d(G)≥c logn/log logn.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02187736
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Embedding of trees in euclidean spaces (1988)
    Springer
    Graphs and combinatorics 4 (1988), S. 43-47 
    Details
    ISSN: 1435-5914
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract It is proved that for any treeT the vertices ofT can be placed on the surface of a sphere inR 3 in such a way that adjacent vertices have distance 1 and nonadjacent vertices have distances less than 1.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01864152
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Realization of cartesian closed topological hulls (1985)
    Springer
    Manuscripta mathematica 53 (1985), S. 1-33 
    Details
    ISSN: 1432-1785
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The cartesian closed topological (CCT) hull of a concrete categoryK is the smallest full CCT extension ofK. A general method for describing the CCT hulls is presented and applied to render unified proofs for the basic examples ofK: topological spaces, uniform spaces, pretopological spaces, compact T2 spaces, metrizable spaces, and completely regular spaces.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01174009
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Banach's Fixed-Point Theorem as a base for data-type equations (1994)
    Springer
    Applied categorical structures 2 (1994), S. 77-90 
    Details
    ISSN: 1572-9095
    Keywords: 68Q65 ; 18D20 ; Data type equation ; complete metric space ; Banach's theorem ; categories enriched over metric spaces
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For a categoryK of data types, solutions of recursive data-type equationsX ℞T(X), whereT is an endofunctor ofK, can be constructed by iteratingT on the unique arrowT1 → 1. This is well-known forK enriched over complete posets and forT locally continuous (an application of the Kleene Fixed-Point Theorem). We prove this forK enriched over complete metric spaces and forT contracting (an application of the Banach Fixed-Point Theorem). Moreover, we prove that each such recursive equation has a unique solution. Our results generalize the approach of P. America and J. Rutten.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00878504
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    Paper (German National Licenses)
    Fulltext
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