Median decompositions arise from any system of vertex cuts via Sageev's dual median graph, are uniquely minimal, satisfy median-width equals clique number on all graphs, and characterize proper geometric actions of groups on median graphs through canonical decompositions of Cayley graphs.
Coning-offCAT(0)cube complexes
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Vertex cuts and median decompositions
Median decompositions arise from any system of vertex cuts via Sageev's dual median graph, are uniquely minimal, satisfy median-width equals clique number on all graphs, and characterize proper geometric actions of groups on median graphs through canonical decompositions of Cayley graphs.