On the shelling antimatroids of split graphs

Unlike poset antimatroids, chordal graph shelling antimatroids have received little attention as regard their structures, optimization properties and associated circuits. Here we consider a special case of those antimatroids, namely the split graph shelling antimatroids. We establish a connection between the structure of split graph shelling antimatroids and poset shelling antimatroids. We discuss some applications of this new connection, in particular, we give a simple polynomial time algorithm to find a maximum weight feasible set in split graph shelling antimatroids.