G-Graphic Delta-Matroids and Their Applications

Abstract

For an abelian group G, a G-labelled graph is a graph whose vertices are labelled by elements of G. We prove that a certain collection of edge sets of a G-labelled graph forms a delta-matroid, which we call a G -graphic delta-matroid, and provide a polynomial-time algorithm to solve the separation problem, which allows us to apply the symmetric greedy algorithm of Bouchet to find a maximum weight feasible set in such a delta-matroid. We present two algorithmic applications on graphs; MAXIMUM WEIGHT PACKING OF TREES OF ORDER NOT DIVISIBLE BY k and MAXIMUM WEIGHT S -TREE PACKING. We also discuss various properties of G-graphic deltamatroids.