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.File in questo prodotto:
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