A family of circuits of a graph G is said to be independent if no two of the circuits have a common vertex; it is called edge-independent if no two of them have an edge in common. A set of vertices will be called a representing set for the circuits (for the sake of brevity we shall call it a representing set), if every circuit of G passes through at least one vertex of the representing set. Denote by I(G) = k the maximum number of circuits in an independent family and by R(G) the minimum number of vertices of a representing set. Dirac and Gallai asked whether there is any relation between I(G) and R(G) (trivially R(G) ≥ I(G)).
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