Minty´s coloured branch theorem versus Tellegen´s theorem

For a directed graph the orthogonality condition of loops and cutsets which is the core of Tellegen´s theorem is shown to be equivalent to the negation of the conjunction of two familiar statements which constitute Minty´s coloured branch theorem. Next, for a directed network a current-voltage formulation of Minty´s theorem is provided and an analogous equivalence with Tellegen´s theorem is established in this setting. Finally, the relationship of these results with the Farkas lemma and the axiomatics of oriented matroids is exhibited. All this confirms an earlier claim made by Narayanan (1985) that Tellegen´s theorem and Minty´s coloured branch theorem are equivalent statements, and rejects a recent absurd argument of Seidel (1995) that they are fundamentally independent