Counting Perfect Matchings in Dense Graphs Is Hard
Data Structures and Algorithms
2022-10-28 v1 Combinatorics
Abstract
We show that the problem of counting perfect matchings remains #P-complete even if we restrict the input to very dense graphs, proving the conjecture in [5]. Here "dense graphs" refer to bipartite graphs of bipartite independence number , or general graphs of independence number . Our proof is by reduction from counting perfect matchings in bipartite graphs, via elementary linear algebra tricks and graph constructions.
Cite
@article{arxiv.2210.15014,
title = {Counting Perfect Matchings in Dense Graphs Is Hard},
author = {Nicolas El Maalouly and Yanheng Wang},
journal= {arXiv preprint arXiv:2210.15014},
year = {2022}
}