On the Representation of a PI-Graph
نویسنده
چکیده
Consider two parallel lines (denoted r1 and r2). A graph is a PI graph (Point-Interval graph) if it is an intersection graph of a family F of triangles between r1 and r2 such that each triangle has an interval with two endpoints on r1 and a vertex (a point) on r2. The family F is the PI representation of G. The PI graphs are an extension of interval and permutation graphs and they form a subclass of trapezoid graphs. In this paper, we characterize the PI graphs in terms of its trapezoid representation. Also we show how to construct a family of trapezoid graphs but not PI graphs from a trapezoid representation of a known graph in this class.
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