Sparsity greedoids and pebble game algorithms for posets
Combinatorics
2026-03-18 v3
Abstract
We generalise a sparsity condition for hypergraphs and show a result relating sparseness of hypergraphs to the decomposition of a modified incidence graph into edge-disjoint forests. We also give new sparsity conditions for posets and define an algorithm of pebble game type for posets to test when these sparsity conditions hold. Furthermore, we prove that under natural conditions, the sparsity conditions define a greedoid.
Keywords
Cite
@article{arxiv.2306.05050,
title = {Sparsity greedoids and pebble game algorithms for posets},
author = {Signe Lundqvist and Tovohery Randrianarisoa and Klara Stokes and Joannes Vermant},
journal= {arXiv preprint arXiv:2306.05050},
year = {2026}
}