Abstract
In this paper we show that an optimal vertex ranking of a permutation graph can be computed in time O(n6), 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.
This research was supported in part by the Office of Naval Research under Grant No. N0014-91-J-1693 and by Deutsche Forschungsgemeinschaft under Kr 1371/1-1.
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© 1994 Springer-Verlag Berlin Heidelberg
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Deogun, J.S., Kloks, T., Kratsch, D., Müller, H. (1994). On vertex ranking for permutation and other graphs. In: Enjalbert, P., Mayr, E.W., Wagner, K.W. (eds) STACS 94. STACS 1994. Lecture Notes in Computer Science, vol 775. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57785-8_187
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DOI: https://doi.org/10.1007/3-540-57785-8_187
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