Matchings and Delta-matroids with coefficients

Delta-matroids are set systems M = (E,F) for a finite set E and 0 not equal F subset of or equal to P(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 Delta-matroids induced by simple graphs. It is shown that these h-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 Delta-matroids; these may also be characterized by some different variant of the Greedy algorithm. Moreover, the structure of the Tutte group of Delta-matroids induced by graphs is completely determined. (C) 1996 Academic Press, Inc.