Arboreal structure and regular graphs of median-like classes
Bostjan Brešar (2003)
Discussiones Mathematicae Graph Theory
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We consider classes of graphs that enjoy the following properties: they are closed for gated subgraphs, gated amalgamation and Cartesian products, and for any gated subgraph the inverse of the gate function maps vertices to gated subsets. We prove that any graph of such a class contains a peripheral subgraph which is a Cartesian product of two graphs: a gated subgraph of the graph and a prime graph minus a vertex. Therefore, these graphs admit a peripheral elimination procedure which...