A Simple Linear Time Algorithm for Triangulating Three-Colored Graphs
نویسندگان
چکیده
In this paper we consider the problem of determining whether a given colored graph can be triangulated, such that no edges between vertices of the same color are added. This problem originated from the Perfect Phylogeny problem from molecular biology, and is strongly related with the problem of recognizing partial k-trees. In this paper we give a simple linear time algorithm that solves the problem when there are three colors. We do this by first giving a complete structural characterization of the class of partial 2-trees. We also give an algorithm that solves the problem for partial 2-trees.
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The analysis showing that our triangulation algorithm runs in linear time is incorrect, and indeed the algorithm does not run in linear time in the worst case. So far we have been unable to obtain a linear-time algorithm for the triangulation problem. We have been able to obtain an 0 (n loglogn)-time algorithm, however. The details are described in ,cAn O(n loglogn)-Time Algorithm for Triangula...
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