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  • 1
    Electronic Resource
    Electronic Resource
    Recognizing the 3-Sphere (1989)
    Oxford, UK : Blackwell Publishing Ltd
    Annals of the New York Academy of Sciences 576 (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.tb16437.x
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  • 2
    Electronic Resource
    Electronic Resource
    Balanced Extensions of 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.tb22471.x
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  • 3
    Electronic Resource
    Electronic Resource
    An Adjacency Criterion for Coxeter Matroids (1999)
    Springer
    Journal of algebraic combinatorics 9 (1999), S. 271-280 
    Details
    ISSN: 1572-9192
    Keywords: matroid ; Coxeter matroid ; Coxeter group ; matroid polytope
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A Coxeter matroid is a generalization of matroid, ordinary matroid being the case corresponding to the family of Coxeter groups A n , which are isomorphic to the symmetric groups. A basic result in the subject is a geometric characterization of Coxeter matroid in terms of the matroid polytope, a result first stated by Gelfand and Serganova. This paper concerns properties of the matroid polytope. In particular, a criterion is given for adjacency of vertices in the matroid polytope.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018600303418
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  • 4
    Electronic Resource
    Electronic Resource
    Graphic matroids, shellability and the Poincare Conjecture (1983)
    Springer
    Geometriae dedicata 14 (1983), S. 303-314 
    Details
    ISSN: 1572-9168
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper we introduce a theory of edge shelling of graphs. Whereas the standard notion of shelling a simplicial complex involves a sequential removal of maximal simplexes, edge shelling involves a sequential removal of the edges of a graph. A necessary and sufficient condition for edge shellability is given in the case of 3-colored graphs, and it is conjectured that the result holds in general. Questions about shelling, and the dual notion of closure, are motivated by topological problems. The connection between graph theory and topology is by way of a complex ΔG associated with a graph G. In particular, every closed 2- or 3-manifold can be realized in this way. If ΔG is shellable, then G is edge shellable, but not conversely. Nevertheless, the condition that G is edge shellable is strong enough to imply that a manifold ΔG must be a sphere. This leads to completely graph-theoretic generalizations of the classical Poincaré Conjecture.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00146910
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  • 5
    Electronic Resource
    Electronic Resource
    Rep-tiling Euclidean space (1995)
    Springer
    Aequationes mathematicae 50 (1995), S. 191-213 
    Details
    ISSN: 1420-8903
    Keywords: Primary 52C20, 52C22 ; Secondary 11A63
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Arep-tiling ℐ is a self replicating, lattice tiling ofR n .Lattice tiling means a tiling by translates of a single compact tile by the points of a lattice, andself-replicating means that there is a non-singular linear mapø: R n → Rn such that, for eachT ∈ ℐ, the imageø(T) is, in turn, tiled by ℐ. This topic has recently come under investigation, not only because of its recreational appeal, but because of its application to the theory of wavelets and to computer addressing. The paper presents an exposition of some recent results on rep-tiling, including a construction of essentially all rep-tilings of Euclidean space. The construction is based on radix representation of points of a lattice. One particular radix representation, called thegeneralized balanced ternary, is singled out as an example because of its relevance to the field of computer vision.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01831118
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  • 6
    Electronic Resource
    Electronic Resource
    Reconstruction of the set of branches of a graph (1996)
    Springer
    Graphs and combinatorics 12 (1996), S. 69-80 
    Details
    ISSN: 1435-5914
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract It is proved that the set of branches of a graphG is reconstructible except in a very special case. More precisely the set of branches of a graphG is reconstructible unless all the following hold: (1) the pruned center ofG is a vertex or an edge, (2)G has exactly two branches, (3) one branch contains all the vertices of degree one ofG and the other branch contains exactly one end-block. This is the best possible result in the sense that in the special excluded case, the reconstruction of the set of branches is equivalent to the reconstruction of the graph itself.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01858446
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  • 7
    Electronic Resource
    Electronic Resource
    The classification of closed surfaces using colored graphs (1993)
    Springer
    Graphs and combinatorics 9 (1993), S. 75-84 
    Details
    ISSN: 1435-5914
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A short graph theoretic proof of the classification of closed surfaces is given. The new proof has the feature that the symmetric canonical graphs for the surfaces do not correspond to the canonical polygons in the usual proof of the classification.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01195329
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