Hilbert Bases of Cuts Hilbert Bases of Cuts
نویسنده
چکیده
Let X be a set of vectors in R m. X is said to be a Hilbert base if every vector in R m which can be written both as a linear combination of members of X with nonnegative coeecients and as a linear combination with integer coeecients can also be written as a linear combination with nonnegative integer coeecients. Denote by H the collection of the graphs whose family of cuts is a Hilbert base. It is known that K 5 and graphs not contractible to K 5 belong to H and that K 6 does not belong to H. We show that every proper subgraph of K 6 belongs to H and that every graph from H is not contractible to K 6. We also study how the class H behaves under several operations.
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