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  • 1
    Electronic Resource
    Electronic Resource
    The Median Stabilization Degree of a Median Algebra (1999)
    Springer
    Journal of algebraic combinatorics 9 (1999), S. 115-127 
    Details
    ISSN: 1572-9192
    Keywords: convex structure ; graphic cube ; median algebra ; median stabilization degree ; superextension
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The median stabilization degree (msd, for short) of a median algebra measures the largest possible number of steps needed to generate a subalgebra with an arbitrary set of generators. We determine the value of msd of a graphic n-cube Qn and we derive an estimation of msd for the natural median operator of Rn which is sharp up to one or two units. Interestingly, msd of Qn and of Rn grows like log1.5n. Finally, we characterize median algebras and median graphs of msd ≤ 1 in terms of forbidden subspaces.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018689708341
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Hereditary modular graphs (1988)
    Springer
    Combinatorica 8 (1988), S. 149-157 
    Details
    ISSN: 1439-6912
    Keywords: 05C38
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In a hereditary modular graphG, for any three verticesu, v, w of an isometric subgraph ofG, there exists a vertex of this subgraph that is simultaneously on some shortestu, v-path,u, w-path andv, w-path. It is shown that the hereditary modular graphs are precisely those bipartite graphs which do not contain any isometric cycle of length greater than four. There is a polynomial-time algorithm available which decides whether a given (bipartite) graph is hereditary modular or not. Finally, the chordal bipartite graphs are characterized by forbidden isometric subgraphs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02122796
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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