# Approximate Schreier decorations and approximate Kőnig’s line coloring Theorem

@article{Grebk2022ApproximateSD, title={Approximate Schreier decorations and approximate Kőnig’s line coloring Theorem}, author={Jan Greb{\'i}k}, journal={Annales Henri Lebesgue}, year={2022} }

Following recent result of L. M. Tóth [arXiv:1906.03137] we show that every 2∆-regular Borel graph G with a (not necessarily invariant) Borel probability measure admits approximate Schreier decoration. In fact, we show that both ingredients from the analogous statements for finite graphs have approximate counterparts in the measurable setting, i.e., approximate König’s line coloring Theorem for Borel graphs without odd cycles and approximate balanced orientation for even degree Borel graphs. It…

## One Citation

Borel fractional colorings of Schreier graphs

- Mathematics
- 2021

. Let Γ be a countable group and let G be the Schreier graph of the free part of the Bernoulli shift Γ ý 2 Γ (with respect to some ﬁnite subset F Ď Γ). We show that the Borel fractional chromatic…

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