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  • 1
    Electronic Resource
    Electronic Resource
    On symmetric and antisymmetric relations (1972)
    Springer
    Monatshefte für Mathematik 76 (1972), S. 323-327 
    Details
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01297365
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    A Note on Maxflow-Mincut and Homomorphic Equivalence in Matroids (2000)
    Springer
    Journal of algebraic combinatorics 12 (2000), S. 295-300 
    Details
    ISSN: 1572-9192
    Keywords: matroids ; strong maps ; homomorphisms ; duality ; Menger's theorem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Graph homomorphisms are used to study good characterizations for coloring problems Trans. Amer. Math. Soc. 384 (1996), 1281–1297; Discrete Math. 22 (1978), 287–300). Particularly, the following concept arises in this context: A pair of graphs (A, B) is called a homomorphism duality if for any graph G either there exists a homomorphism σ : A → G or there exists a homomorphism τ : G → B but not both. In this paper we show that maxflow-mincut duality for matroids can be put into this framework using strong maps as homomorphisms. More precisely, we show that, if C k denotes the circuit of length k + 1, the pairs (C k , C k + 1) are the only homomorphism dualities in the class of duals of matroids with the strong integer maxflow-mincut property (Jour. Comb. Theor. Ser.B 23 (1977), 189–222). Furthermore, we prove that for general matroids there is only a trivial homomorphism duality.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1011268025029
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  • 3
    Electronic Resource
    Electronic Resource
    Random graphs and covering graphs of posets (1986)
    Springer
    Order 3 (1986), S. 245-255 
    Details
    ISSN: 1572-9273
    Keywords: 06A10 ; 60C05 ; Poset ; diagram ; covering graph ; random graph
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For a graph G, we define c(G) to be the minimal number of edges we must delete in order to make G into a covering graph of some poset. We prove that, if p=n -1+η(n) ,where η(n) is bounded away from 0, then there is a constant k 0〉0 such that, for a.e. G p , c(G p )≥k 0 n 1+η(n) .In other words, to make G p into a covering graph, we must almost surely delete a positive constant proportion of the edges. On the other hand, if p=n -1+η(n) , where η(n)→0, thenc(G p )=o(n 1+η(n) ), almost surely.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00400288
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  • 4
    Electronic Resource
    Electronic Resource
    Complexity of diagrams (1987)
    Springer
    Order 3 (1987), S. 321-330 
    Details
    ISSN: 1572-9273
    Keywords: 06A10 ; Poset ; diagram ; NP-completeness
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A diagram is an undirected graph corresponding to the covering relation of a finite poset. We prove that three decision problems related to diagrams are NP-complete.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00340774
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  • 5
    Electronic Resource
    Electronic Resource
    Chromatic number of Hasse diagrams, eyebrows and dimension (1991)
    Springer
    Order 8 (1991), S. 41-48 
    Details
    ISSN: 1572-9273
    Keywords: 05C15 ; 05C20 ; 06A06 ; Chromatic number ; partially ordered sets ; dimension ; Hasse diagrams
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We construct posets of dimension 2 with highly chromatic Hasse diagrams. This solves a previous problem by Nesetril and Trotter.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00385813
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  • 6
    Electronic Resource
    Electronic Resource
    Complexity of diagrams (1993)
    Springer
    Order 10 (1993), S. 393-393 
    Details
    ISSN: 1572-9273
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01108833
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  • 7
    Electronic Resource
    Electronic Resource
    Combinatorial partitions of finite posets and lattices —Ramsey lattices (1984)
    Springer
    Algebra universalis 19 (1984), S. 106-119 
    Details
    ISSN: 1420-8911
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It is proved that for every finite latticeL there exists a finite latticeL′ such that for every partition of the points ofL′ into two classes there exists a lattice embeddingf:L→L′ such that the points off(L) are in one of the classes. This property is called point-Ramsey property of the class of all finite lattices. In fact a stronger theorem is proved which implies the following: for everyn there exists a finite latticeL such that the Hasse-diagram (=covering relation) has chromatic number 〉n. We discuss the validity of Ramseytype theorems in the classes of finite posets (where a full discussion is given) and finite distributive lattices. Finally we prove theorems which deal with partitions of lattices into an unbounded number of classes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01191498
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  • 8
    Electronic Resource
    Electronic Resource
    On critical uniquely colorable graphs (1972)
    Springer
    Archiv der Mathematik 23 (1972), S. 210-213 
    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/BF01304871
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    Paper (German National Licenses)
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  • 9
    Electronic Resource
    Electronic Resource
    Finite union theorem with restrictions (1986)
    Springer
    Graphs and combinatorics 2 (1986), S. 357-361 
    Details
    ISSN: 1435-5914
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The aim of this paper is to prove the following extension of the Folkman-Rado-Sanders Finite Union Theorem: For every positive integersr andk there exists a familyL of sets having the following properties: i) ifS 1,S 2, ...,S k + 1 are distinct pariwise disjoint elements ofL then there exists nonemptyI ⊂ {1, 2, ...,k + 1} with ∪ i∈I S i ⋃L ii) ifL =L 1 ⋃...⋃L r is an arbitrary partition then there existsj ≤ r and pairwise disjoint setsS 1,S 2, ...,S k ∈L j , such thatL i∈I S i ∈L j for every nonemptyI ⊂ {1, 2, ...,k}.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01788110
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  • 10
    Electronic Resource
    Electronic Resource
    On sets of integers with the Schur property (1986)
    Springer
    Graphs and combinatorics 2 (1986), S. 269-275 
    Details
    ISSN: 1435-5914
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We investigate sets of integers for which Rado and Schur theorems are true from the point of view of their local density. We establish the existence of locally sparse Rado and Schur sets in a strong sense.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01788101
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    Paper (German National Licenses)
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