Expander spanning subgraphs with large girth
Combinatorics
2021-12-04 v1 Metric Geometry
Probability
Abstract
We conjecture that finite graphs with positive Cheeger constant admit a spanning subgraph with positive Cheeger constant and girth proportional to the diameter. We prove this conjecture for regular expander graphs with large expansion. Our proof relies on the Local Lemma.
Keywords
Cite
@article{arxiv.2012.15502,
title = {Expander spanning subgraphs with large girth},
author = {Itai Benjamini and Mikolaj Fraczyk and Gabor Kun},
journal= {arXiv preprint arXiv:2012.15502},
year = {2021}
}
Comments
11 pages. arXiv admin note: substantial text overlap with arXiv:1303.4982