Distance visibility graphs

DISTANCE VISIBILITY GRAPHS Collette Coullard Dept. of Industrial Engineering and Management Sciences Northwestern University Evanston, Illinois, USA coullard@iems. rtwu. edu Anna Lubiw Dept. of Computer Science University of Waterloo Waterloo, Ontario, Canada, N2L 3G1 alubiw@aater. waterloo, edu A new necessary condition for a graph G to be the visibility graph of a simple polygon is given: each 3connected component of G must. have a vertex ordering in which every vertex is adjacent to a previous 3-clique. This property is used to give an algorithm for the distance visibility graph problem: given an edge-weighted graph G, is it the visibility graph of a simple polygon with the given weights as Euclidean distances?

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