Jan Fricke
Published 2016-07-25Version 1
Assume that there is a free group action of automorphisms on a bipartite graph. If there is a perfect matching on the factor graph, then obviously there is a perfect matching on the graph. Surprisingly, the reversed is also true for amenable groups: if there is a perfect matching on the graph, there is also a perfect matching on the factor graph, i. e. a group invariant ("symmetric") perfect matching on the graph.
Bounded projections to the $\mathcal{Z}$-factor graph
Symmetric graphs of prime valency with a transitive simple group
On the orders of arc-transitive graphs
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