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  • 1
    Electronic Resource
    Electronic Resource
    The maximum number of Hamiltonian paths in tournaments (1990)
    Springer
    Combinatorica 10 (1990), S. 319-324 
    Details
    ISSN: 1439-6912
    Keywords: 05 C 20 ; 05 C 35 ; 05 C 38
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Solving an old conjecture of Szele we show that the maximum number of directed Hamiltonian paths in a tournament onn vertices is at mostc · n 3/2 · n!/2 n−1, wherec is a positive constant independent ofn.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02128667
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    A lattice point problem and additive number theory (1995)
    Springer
    Combinatorica 15 (1995), S. 301-309 
    Details
    ISSN: 1439-6912
    Keywords: 11 B 75
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For every dimensiond≥1 there exists a constantc=c(d) such that for alln≥1, every set of at leastcn lattice points in thed-dimensional Euclidean space contains a subset of cardinality preciselyn whose centroid is also a lattice point. The proof combines techniques from additive number theory with results about the expansion properties of Cayley graphs with given eigenvalues.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01299737
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Star arboricity (1992)
    Springer
    Combinatorica 12 (1992), S. 375-380 
    Details
    ISSN: 1439-6912
    Keywords: 05 C 70 ; 60 C 05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Astar forest is a forest all of whose components are stars. Thestar arboricity, st(G) of a graphG is the minimum number of star forests whose union covers all the edges ofG. Thearboricity, A(G), of a graphG is the minimum number of forests whose union covers all the edges ofG. Clearlyst(G)≥A(G). In fact, Algor and Alon have given examples which show that in some casesst(G) can be as large asA(G)+Ω(logΔ) (where Δ is the maximum degree of a vertex inG). We show that for any graphG, st(G)≤A(G)+O(logΔ).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01305230
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    Paper (German National Licenses)
    Fulltext
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