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  • 1975-1979  (1)
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    Electronic Resource
    Electronic Resource
    On the integer-valued variables in the linear vertex packing problem (1977)
    Springer
    Mathematical programming 12 (1977), S. 97-101 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Given a graph with weights on vertices, the vertex packing problem consists of finding a vertex packing (i.e. a set of vertices, no two of them being adjacent) of maximum weight. A linear relaxation of one binary programming formulation of this problem has these two well-known properties: (i) every basic solution is (0, 1/2, 1)-valued, (ii) in an optimum linear solution, an integer-valued variable keeps the same value in an optimum binary solution. As an answer to an open problem from Nemhauser and Trotter, it is shown that there is a unique maximal set of variables which are integral in optimal (VLP) solutions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01593772
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