A note on range-restricted circuit covers

Rizzi, Romeo (1999) A note on range-restricted circuit covers. UNSPECIFIED.

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    Abstract

    Let Cone(G), Int.Cone(G) and Lat(G) be the cone, the integer cone and the lattice of the incidence vectors of the circuits of graph G. A good range is a set K of natural numbers such that the intersection of Cone(G), Lat(G) and K^E is contained in Int.Cone(G) for every graph G=(V,E). We give a counterexample to a conjecture of Goddyn [ Goddyn, L.A.: Cones, Lattices and Hilbert Bases of Circuits and Perfect Matchings. Contemporary Mathematics 147, 419--439 (1993)] stating that N\{1} is a good range.

    Item Type: Departmental Technical Report
    Department or Research center: Information Engineering and Computer Science
    Subjects: Q Science > QA Mathematics > QA075 Electronic computers. Computer science
    Uncontrolled Keywords: range-restricted circuit covers, Petersen graph, Hilbert basis
    Additional Information: Published in: "Graphs and Combinatorics" vol. 16 (2000) 355--358.
    Report Number: DIT-02-056
    Repository staff approval on: 21 Jan 2003

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