Some Structure Theory for Cayley Graphs and Associated Hypergraphs

We expand the structural theory of \ca graphs that avoid specific cyclic coset patterns. We present several characterisations of tree-likeness for these structures and show a close connection to $\alpha$-acyclic hypergraphs. A focus lies on the behaviour of short paths of overlapping cosets in these \ca graphs, and their relation to short chordless paths in hypergraphs that are locally acyclic.