The computational strength of matchings in countable graphs
Abstract
In a 1977 paper, Steffens identified an elegant criterion for determining when a countable graph has a perfect matching. In this paper, we will investigate the proof-theoretic strength of this result and related theorems. We show that a number of natural variants of these theorems are equivalent, or closely related, to the ``big five'' subsystems of reverse mathematics. The results of this paper explore the relationship between graph theory and logic by showing the way in which specific changes to a single graph-theoretic principle impact the corresponding proof-theoretical strength. Taken together, the results and questions of this paper suggest that the existence of matchings in countable graphs provides a rich context for understanding reverse mathematics more broadly.
Keywords
Cite
@article{arxiv.2006.11334,
title = {The computational strength of matchings in countable graphs},
author = {Stephen Flood and Matthew Jura and Oscar Levin and Tyler Markkanen},
journal= {arXiv preprint arXiv:2006.11334},
year = {2020}
}
Comments
38 pages, 5 figures