Some Structure Theory for Cayley Graphs and Associated Hypergraphs
Abstract
We expand the structural theory of graphs that avoid specific cyclic coset patterns. We present several characterisations of tree-likeness for these structures and show a close connection to α-acyclic hypergraphs. A focus lies on the behaviour of short paths of overlapping cosets in these graphs, and their relation to short chordless paths in hypergraphs that are locally acyclic.
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