Stability in circular arc graphs
Journal of Algorithms
Graph classes: a survey
Modular decomposition and transitive orientation
Discrete Mathematics - Special issue on partial ordered sets
Stable sets in certain P6-free graphs
Discrete Applied Mathematics
A note on &agr;-redundant vertices in graphs
Discrete Applied Mathematics
On linear and circular structure of (claw, net)-free graphs
Discrete Applied Mathematics
On easy and hard hereditary classes of graphs with respect to the independent set problem
Discrete Applied Mathematics - Special issue on stability in graphs and related topics
Augmenting graphs for independent sets
Discrete Applied Mathematics - The fourth international colloquium on graphs and optimisation (GO-IV)
New applications of clique separator decomposition for the Maximum Weight Stable Set problem
Theoretical Computer Science
Maximum independent sets in graphs of low degree
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
On clique separators, nearly chordal graphs, and the Maximum Weight Stable Set Problem
Theoretical Computer Science
A polynomial algorithm to find an independent set of maximum weight in a fork-free graph
Journal of Discrete Algorithms
New applications of clique separator decomposition for the maximum weight stable set problem
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
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Clique separators in graphs are a helpful tool used by Tarjan as a divide-and-conquer approach for solving various graph problems such as the Maximum Weight Stable Set (MWS) Problem, Coloring and Minimum Fill-in but few examples are known where this approach was used. We combine decomposition by clique separators and by homogeneous sets and show that the resulting binary tree gives an efficient way for solving the MWS problem. Moreover, we combine this approach with the concept of nearly chordal and nearly perfect and obtain some new graph classes where MWS is solvable in polynomial time by our approach. On some of these classes, the unweighted Maximum Stable Set (MS) Problem was known to be solvable in polynomial time by the struction method or by augmenting techniques, respectively, but the complexity of the MWS problem was open. A graph is nearly chordal if for each of its vertices, the subgraph induced by the set of its nonneighbors is chordal, and analogously for nearly perfect graphs.