It can happen that two equivariant sets with atoms are related by a finitely supported bijection, but not by an equivariant bijection.
Tag Archives: anomalies
Bipartite graphs without bipartite partition
In the equality symmetry, there is a single-orbit graph with the property that
is bipartite in the classical sense (equivalently, has no odd-length cycle) but has no partition into two parts which are finitely supported and not inter-connected. In other words, the graph
maps to the single-edge graph via a infinitely-supported homomorphism, but not via a finitely-supported one. And here’s the graph: its nodes are pairs of distinct atoms, and there is an edge from
to
, whenever
are distinct atoms. That’s it.