# Atoms of the matching measure

@article{Bencs2020AtomsOT, title={Atoms of the matching measure}, author={Ferenc Bencs and Andr'as M'esz'aros}, journal={Electronic Journal of Probability}, year={2020} }

We prove that the matching measure of an infinite vertex-transitive connected graph has no atoms. Generalizing the results of Salez, we show that for an ergodic non-amenable unimodular random rooted graph with uniformly bounded degrees, the matching measure has only finitely many atoms. Ku and Chen proved the analogue of the Gallai-Edmonds structure theorem for non-zero roots of the matching polynomial for finite graphs. We extend their results for infinite graphs. We also show that the…

## One Citation

### A refined Gallai-Edmonds structure theorem for weighted matching polynomials

- MathematicsDiscret. Math.
- 2023

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