12 research outputs found
Nested hierarchies in planar graphs
We construct a partial order relation which acts on the set of 3-cliques of a
maximal planar graph G and defines a unique hierarchy. We demonstrate that G is
the union of a set of special subgraphs, named `bubbles', that are themselves
maximal planar graphs. The graph G is retrieved by connecting these bubbles in
a tree structure where neighboring bubbles are joined together by a 3-clique.
Bubbles naturally provide the subdivision of G into communities and the tree
structure defines the hierarchical relations between these communities
2nd Annual Computer & Technology Law Institute
Materials from the 2nd Annual Computer & Technology Law Institute held by UK/CLE in March 2000