We prove that every non-amenable Cayley graph admits a factor of IID perfect matching. We also show that any connected d-regular vertex transitive graph admits a perfect matching. The two results together imply that every Cayley graph admits an invariant random perfect matching.
1
University of Warwick, Coventry, UK
2
Northeastern University, Boston, USA
Endre Csóka; Gabor Lippner. Invariant random perfect matchings in Cayley graphs. Groups, geometry, and dynamics, Tome 11 (2017) no. 1, pp. 211-243. doi: 10.4171/ggd/395
@article{10_4171_ggd_395,
author = {Endre Cs\'oka and Gabor Lippner},
title = {Invariant random perfect matchings in {Cayley} graphs},
journal = {Groups, geometry, and dynamics},
pages = {211--243},
year = {2017},
volume = {11},
number = {1},
doi = {10.4171/ggd/395},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/395/}
}
TY - JOUR
AU - Endre Csóka
AU - Gabor Lippner
TI - Invariant random perfect matchings in Cayley graphs
JO - Groups, geometry, and dynamics
PY - 2017
SP - 211
EP - 243
VL - 11
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/395/
DO - 10.4171/ggd/395
ID - 10_4171_ggd_395
ER -
%0 Journal Article
%A Endre Csóka
%A Gabor Lippner
%T Invariant random perfect matchings in Cayley graphs
%J Groups, geometry, and dynamics
%D 2017
%P 211-243
%V 11
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/395/
%R 10.4171/ggd/395
%F 10_4171_ggd_395
