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Large vertex-flames in uncountable digraphs
[article]
2022
arXiv
pre-print
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 κ_D(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 κ_L(r,v)=κ_D(r,v) for every v∈ V-r must have at least ∑_v∈ V-rκ_D(r,v) edges. Lovász proved that, maybe surprisingly, this lower bound is
arXiv:2107.12935v3
fatcat:rwhktnij5jex5kqdsxy5f44cgm