DocumentCode :
2243832
Title :
Minty´s coloured branch theorem versus Tellegen´s theorem
Author :
Cel, J.
Author_Institution :
Tech. Univ. Lodz, Poland
Volume :
1
fYear :
2000
fDate :
2000
Firstpage :
204
Abstract :
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
Keywords :
directed graphs; network topology; Farkas lemma; Minty coloured branch theorem; Tellegen theorem; axiomatics; current-voltage formulation; cutsets; directed graph; directed network; loops; oriented matroids; orthogonality condition; Kirchhoff´s Law; Set theory;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Circuits and Systems, 2000. Proceedings. ISCAS 2000 Geneva. The 2000 IEEE International Symposium on
Conference_Location :
Geneva
Print_ISBN :
0-7803-5482-6
Type :
conf
DOI :
10.1109/ISCAS.2000.857063
Filename :
857063
Link To Document :
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