Matchings and Δ-matroids with coefficients

Abstract

Δ-matroids are set systems M = (E,ℱ) for a finite set E and Ø ≠ ℱ ⊆ ℬ (E) which may be characterized by some variant of the Greedy algorithm for solving optimization problems. This paper is devoted to the examination of the particular subclass of Δ-matroids induced by simple graphs. It is shown that these Δ-matroids are representable over fields of any characteristic and that weightings defined on the edge set and with values in some linearly ordered abelian group give rise to valuated Δ-matroids; these may also be characterized by some different variant of the Greedy algorithm. Moreover, the structure of the Tutte group of Δ-matroids induced by graphs is completely determined. © 1996 Academic Press, Inc.