Abstract
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 coefficients and as a linear combination with integer coefficients can also be written as a linear combination with nonnegative integer coefficients. Denote by H the collection of the graphs whose family of cuts is a Hilbert base. It is known that K 5 and graphs with no K 5- minor 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 does not have K 6 as a minor. We also study how the class H behaves under several operations.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
