Coloring planar perfect graphs by decomposition
Combinatorica
Decomposition of perfect graphs
Journal of Combinatorial Theory Series B
Recognizing planar perfect graphs
Journal of the ACM (JACM)
Graphs and Hypergraphs
The structure of bull-free graphs I-Three-edge-paths with centers and anticenters
Journal of Combinatorial Theory Series B
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Efficient decomposition algorithms for the weighted maximum independent set, minimum coloring, and minimum clique cover problems on planar perfect graphs are presented. These planar graphs can also be characterized by the absence of induced odd cycles of length greater than 3 (odd holes). The algorithm in this paper is based on decomposing these graphs into essentially two special classes of inseparable component graphs whose optimization problems are easy to solve, finding the solutions for these components and combining them to form a solution for the original graph. These two classes are (i) planar comparability graphs and (ii) planar line graphs of those planar bipartite graphs whose maximum degrees are no greater than three. The same techniques can be applied to other classes of perfect graphs, provided that efficient algorithms are available for their inseparable component graphs.