On the shelling antimatroids of split graphs
Discrete Mathematics
2023-06-22 v3 Data Structures and Algorithms
Combinatorics
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.
Keywords
Cite
@article{arxiv.1512.06073,
title = {On the shelling antimatroids of split graphs},
author = {Jean Cardinal and Jean-Paul Doignon and Keno Merckx},
journal= {arXiv preprint arXiv:1512.06073},
year = {2023}
}