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  • 1
    Electronic Resource
    Electronic Resource
    Highly linked graphs (1996)
    Springer
    Combinatorica 16 (1996), S. 313-320 
    Details
    ISSN: 1439-6912
    Keywords: 05 C 40 ; 05 C 38
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A graph with at least 2k vertices is said to bek-linked if, for any choices 1,...,s k ,t 1,...,t k of 2k distinct vertices there are vertex disjoint pathsP 1,...,P k withP i joinings i tot i , 1≤i≤k. Recently Robertson and Seymour [16] showed that a graphG isk-linked provided its vertex connectivityk(G) exceeds $$10k\sqrt {\log _2 k}$$ . We show here thatk(G)≥22k will do.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01261316
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Cycles through specified vertices (1993)
    Springer
    Combinatorica 13 (1993), S. 147-155 
    Details
    ISSN: 1439-6912
    Keywords: 05 C 38
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Recently, various authors have obtained results about the existence of long cycles in graphs with a given minimum degreed. We extend these results to the case where only some of the vertices are known to have degree at leastd, and we want to find a cycle through as many of these vertices as possible. IfG is a graph onn vertices andW is a set ofw vertices of degree at leastd, we prove that there is a cycle through at least $$\left\lceil {\frac{w}{{\left\lceil {{n \mathord{\left/ {\vphantom {n d}} \right. \kern-\nulldelimiterspace} d}} \right\rceil - 1}}} \right\rceil $$ vertices ofW. We also find the extremal graphs for this property.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01303200
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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