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  • Articles: DFG German National Licenses  (5)
Source
Material
Years
  • 1
    Electronic Resource
    Electronic Resource
    Independent Trees in Planar Graphs Independent trees (1999)
    Springer
    Graphs and combinatorics 15 (1999), S. 29-77 
    Details
    ISSN: 1435-5914
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract.  We prove the following statement: Let G be a finite k-connected undirected planar graph and s be a vertex of G. Then there exist k spanning trees T 1,…,T k in G such that for each vertex x≠s of G, the k paths from x to s in T 1,…,T k are pairwise openly disjoint.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s003730050030
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Independent trees in graphs (1994)
    Springer
    Graphs and combinatorics 10 (1994), S. 29-45 
    Details
    ISSN: 1435-5914
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract IfG is a finite undirected graph ands is a vertex ofG, then two spanning treesT 1 andT 2 inG are calleds — independent if for each vertexx inG the paths fromx tos inT 1 andT 2 are openly disjoint. It is known that the following statement is true fork≤3: IfG isk-connected, then there arek pairwises — independent spanning, trees inG. As a main result we show that this statement is also true fork=4 if we restrict ourselves to planar graphs. Moreover we consider similar statements for weaklys — independent spanning trees (i.e., the tree paths from a vertex tos are edge disjoint) and for directed graphs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01202468
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Independent Trees and Branchings in Planar Multigraphs (1999)
    Springer
    Graphs and combinatorics 15 (1999), S. 211-220 
    Details
    ISSN: 1435-5914
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract.  The following statement is proved: Let G be a finite directed or undirected planar multigraph and s be a vertex of G such that for each vertex x≠s of G, there are at least k pairwise openly disjoint paths in G from x to s where k∉{3,4,5} if G is directed. Then there exist k spanning trees T 1, … ,T k in G directed towards s if G is directed such that for each vertex x≠s of G, the k paths from x to s in T 1, … ,T k are pairwise openly disjoint. – The case where G is directed and k∈{3,4,5} remains open.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s003730050041
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    Paper (German National Licenses)
    Fulltext
  • 4
    Electronic Resource
    Electronic Resource
    A sufficient condition for graphs to be weaklyk-linked (1991)
    Springer
    Graphs and combinatorics 7 (1991), S. 323-351 
    Details
    ISSN: 1435-5914
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We consider graphs, which are finite, undirected, without loops and in which multiple edges are possible. For each natural numberk letg(k) be the smallest natural numbern, so that the following holds: LetG be ann-edge-connected graph and lets 1,...,s k,t 1,...,t k be vertices ofG. Then for everyi ∈ {1,..., k} there existsa pathP i froms i tot i, so thatP 1,...,P k are pairwise edge-disjoint. We prove $$g\left( k \right) \leqslant \left\{ {\begin{array}{*{20}c} {k + 1, if k is odd} \\ {k + 2, if k is even} \\ \end{array} } \right.$$
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01787639
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Counterexamples to a conjecture of mader about cycles through specified vertices inn-edge-connected graphs (1992)
    Springer
    Graphs and combinatorics 8 (1992), S. 253-258 
    Details
    ISSN: 1435-5914
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract For each oddn≥3, we constructn-edge-connected graphsG with the following property: There are two verticesu andv inG such that for every cycleC inG passign throughu andv the graphG-E(C) is not (n-2)-edge-connected. HereE(C) denotes the set of edges ofC, and a cycle is allowed to pass through a vertex more than once.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02349962
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    Paper (German National Licenses)
    Fulltext
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