The delta-sum of matching delta-matroids
A delta-matroid is a pair \(D= (V,{\mathcal F})\), where \(V\) is a finite set and \({\mathcal F}\) is a nonempty collection of subsets of \(V\) satisfying the symmetric exchange axiom: For \(F_1,F_2\in{\mathcal F}\) and \(x\in F_1\Delta F_2\), there exists \(y\in F_1\Delta F_2\) such that \(F_1\Delta\{x, y\}\in{\mathcal F}\). The authors discuss a composition operation of delta-matroids, called delta-sum, namely: If \((V,{\mathcal F}_i)\), \(i= 1, 2\), are delta-matroids, then \((V,{\mathcal F}_1\Delta{\mathcal F}_2)\), where \({\mathcal F}_1\Delta{\mathcal F}_2= \{F_1\Delta F_2\mid F_1\in{\mathcal F}_1\) and \(F_2\in{\mathcal F}_2\}\), is also a delta-matroid. The delta-sum of matching delta-matroids is associated with the linkings of a graph. A min-max rank function of that delta-matroids, together with some applications of it on linkings are given in the last section of the paper.
scientific article; zbMATH DE number 1135957