  For an abelian group $\Gamma$, a $\Gamma$-labelled graph is a graph whose
vertices are labelled by elements of $\Gamma$. We prove that a certain
collection of edge sets of a $\Gamma$-labelled graph forms a delta-matroid,
which we call a $\Gamma$-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 $\Gamma$-graphic
delta-matroids.
