Circular representation problem on hypergraphs

A hypergraph J=(X,E) is said to be circular representable, if its vertices can be placed on a circle, in such way that every edge of H induces an interval. This concept is a translation into the vocabulary of hypergraphs of the circular one's property for the (0, 1) matrices [6] studied by Tucker [9, 10]. We give here a characterization of the hypergraphs which are circular representable. We study when the associated representation is unique, and we characterize the possible transformations of a representation into another, a kind of problem which has already been treated from the algorithmic point of view by Booth and Lueker [1] or Duchet [2] in the case of the interval representable hypergraphs.Finally, we establish a connection between circular graphs and circular representable hypergraphs of the type of the Fulkerson-Gross connection between interval graphs and matrices having the consecutive one's property [5], in some special cases.