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# Canonical decompositions of symmetric submodular systems

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## Abstract

Let E be a finite set, R the set of real numbers and f: 2^{E} → R a symmetric submodular function. The pair (E,f) is called a symmetric submodular system. We examine the structures of symmetric submodular systems and provide a decomposition theory of symmetric submodular systems. The theory is a generalization of the decomposition theory of 2-connected graphs developed by W. T. Tutte.

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## Copyright information

© Springer-Verlag Berlin Heidelberg 1981