Euler Diagrams

(Anne Verroust-Blondet)

Version française




 We want to use diagrams  to visualize the results of a complex request inside a graphical interface for traditional library environments. Such a representation allows the user to perceive simultaneously the results of his query and the relevance of the database according to the query.
We have shown by a constructive method the existence of a planar diagrammatic representation called extended Euler diagrams, derived from the Euler diagram representation, for any collection of sets X1,...,Xn , n < 9.  These diagrams are adapted for representing sets inclusions and intersections: each set Xi and each non empty intersection of a subcollection of X1,...,Xn is represented by a unique connected region of the plane.
Moreover, using the notion of planarity and drawing for hypergraphs introduced respectively by Johnson and Pollak in 1987 and Mäkinen in 1990, we have shown that any hypergraph having less than nine hyperedges is vertex-planar and can be drawn in the edge standard and in the subset standard without edge crossing.


euler diagram exampleanother euler diagram example



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