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On the structure of trapezoid graphs. (English) Zbl 0849.05060
Consider two parallel lines each containing n intervals, labelled 1 to n, where two intervals with the same label define a trapezoid with that label. The intersection graph of such a set of trapezoids is called a trapezoid graph. Trapezoid graphs contain both permutation graphs and interval graphs. The paper deals with an operation called vertex splitting which allows to transform a trapezoid graph into a permutation graph with special properties. This implies an O(n 3 ) algorithm for recognizing a trapezoid graph. The algorithm is slower than Ma’s algorithm, see T.-H. Ma and J. P. Spinrad [Lect. Notes Comput. Sci. 484, 61-71 (1992; Zbl 0768.68162)], put conceptually simpler and easier to code.
Reviewer: G.Gutin (Odense)

05C85Graph algorithms (graph theory)
05C99Graph theory