On the shelling antimatroids of split graphs

TL;DR

This paper studies split graph shelling antimatroids, revealing their connection to poset shelling antimatroids, and provides algorithms and structural insights for optimization and combinatorial properties.

Contribution

It introduces the structure of split graph shelling antimatroids, relates them to poset shelling antimatroids, and offers polynomial algorithms and structural characterizations.

Findings

Feasible sets relate to poset shelling antimatroids.

Polynomial-time algorithm for maximum weight feasible set.

Description of circuits and free sets.

Abstract

Chordal graph shelling antimatroids have received little attention with regard to their combinatorial properties and related optimization problems, as compared to the case of poset shelling antimatroids. Here we consider a special case of these antimatroids, namely the split graph shelling antimatroids. We show that the feasible sets of such an antimatroid relate to some poset shelling antimatroids constructed from the graph. We discuss a few applications, obtaining in particular a simple polynomial-time algorithm to find a maximum weight feasible set. We also provide a simple description of the circuits and the free sets.