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 $R$ of natural numbers such that Cone(G) \cap Lat(G) \cap R^E \subseteq Int.Cone(G) for every graph G(V,E). We give a counterexample to a conjecture of Goddyn stating that by simply removing 1 from the naturals we get a good range.

A note on range-restricted circuit covers

RIZZI, ROMEO
2000-01-01

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 $R$ of natural numbers such that Cone(G) \cap Lat(G) \cap R^E \subseteq Int.Cone(G) for every graph G(V,E). We give a counterexample to a conjecture of Goddyn stating that by simply removing 1 from the naturals we get a good range.
2000
range-restricted circuit covers; Petersen graph; Hilbert basis
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/409605
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