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On vertex ranking for permutation and other graphs. (English) Zbl 0941.05516
Enjalbert, Patrice (ed.) et al., STACS 94. 11th Annual Symposium on Theoretical Aspects of Computer Science, Caen, France, February 24-26, 1994. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 775, 747-758 (1994).
Summary: In this paper we show that an optimal vertex ranking of a permutation graph can be computed in time $$O(n^6)$$, where $$n$$ is the number of vertices. The demonstrated minimal separator approach can also be used for designing polynomial-time algorithms computing an optimal vertex ranking on the following classes of well-structured graphs: circular permutation graphs, interval graphs, circular arc graphs, trapezoid graphs and cocomparability graphs of bounded dimension.
For the entire collection see [Zbl 0825.00118].

##### MSC:
 05C85 Graph algorithms (graph-theoretic aspects) 68Q25 Analysis of algorithms and problem complexity