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  • 1
    Electronic Resource
    Electronic Resource
    Subgraphs of hypercubes and subdiagrams of boolean lattices (1996)
    Springer
    Order 13 (1996), S. 41-64 
    Details
    ISSN: 1572-9273
    Keywords: 05C10 ; 06A07 ; 05C78 ; 68Q10 ; Boolean lattice ; hypercube ; embedding ; coloring
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper we extensively treat the following problems: When is a given graph a subgraph (resp. induced subgraph) of a hypercube and when is an ordered set a subdiagram (resp. induced subdiagram) of a Boolean lattice? We present characterizations for that in terms of suitable edge-colorings of the graphs and, for ordered sets, of their covering graphs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00383967
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Counting formulas for glued lattices (1985)
    Springer
    Order 1 (1985), S. 265-276 
    Details
    ISSN: 1572-9273
    Keywords: 05A15 ; 06B05 ; Incidence structure ; graph ; glued lattice ; glued tolerance relation ; skeleton ; Dilworth's theorem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A tolerance relation θ of a lattice L, i.e., a reflexive and symmetric relation of L which is compatible with join and meet, is called glued if covering blocks of θ have nonempty intersection. For a lattice L with a glued tolerance relation we prove a formula counting the number of elements of L with exactly k lower (upper) covers. Moreover, we prove similar formulas for incidence structures and graphs and we give a new proof of Dilworth's covering theorem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00383603
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    Paper (German National Licenses)
    Fulltext
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