This gives an analogue of the Morrey-Sobolev embedding theorem W2,p(Rml) ⊆ C1,α (Rml) but, more importantly, we also obtain a qualitative control over the local graph representations of Σ only in terms of the energyEBSCO_AspTransactions of the American Mathematical Society...
Theorem 3.1. (Aharoni 1987) G satisfies the Erd˝os-Menger conjecture for all sets A, B ⊆ V . When proving Theorem 3.1 one may clearly assume that Z := A∩B = ∅: having solved the problem for G−Z, just add every z ∈ Z to X and, as a singleton path { z }, ...