Delta-matroids

Conference · Fri Dec 30 23:00:00 EST 1994

OSTI ID:36055

Geelan, J ^[1]

---

1. Univ. of Waterloo (Canada)

A delta-matroid is a set system (V, F) satisfying the symmetric exchange axiom: for all X, Y {element_of} F and x {element_of} Y {delta} X there exists y {element_of} X{delta}Y such that X{delta}{l_brace}x, y{r_brace} {element_of} F ({delta} denotes symmetric difference). This is a relaxation of the exchange axiom for the bases of matroids. The following example of a class of delta-matroids is a generalization of the class of linear matroids: Let A be a symmetric (or skew symmetric) matrix whose rows and columns are both indexed by V, and define F{sub A} to be the collection of subsets of V that index the nonsingular principal submatrices of A. Bouchet proved that (V, F{sub A}) is a delta-matroid. We consider some algorithmic and theoretical question that arises naturally through this generalization.

• OSTI ID: 36055
• Report Number(s): CONF-9408161--
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ALGORITHMS
EFFICIENCY
MATRICES
NUMERICAL SOLUTION