# Large vertex-flames in uncountable digraphs

@inproceedings{Gut2021LargeVI, title={Large vertex-flames in uncountable digraphs}, author={Florian Gut and Attila Jo'o}, year={2021} }

The study of minimal subgraphs witnessing a connectivity property is an important field in graph theory. The foundation for large flames has been laid by Lovász: Let D = (V,E) be a finite digraph and let r ∈ V . The local connectivity κD(r, v) from r to v is defined to be the maximal number of internally disjoint r → v paths in D. A spanning subdigraph L of D with κL(r, v) = κD(r, v) for every v ∈ V − r must have at least ∑ v∈V−r κD(r, v) edges. Lovász proved that, maybe surprisingly, this… Expand

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