On generating all maximal independent sets
Information Processing Letters
Stability in circular arc graphs
Journal of Algorithms
On diameters and radii of bridged graphs
Discrete Mathematics
On the complexity of recognizing perfectly orderable graphs
Discrete Mathematics
Computing independent sets in graphs with large girth
Discrete Applied Mathematics
Stability number of bull- and chair-free graphs
Discrete Applied Mathematics
Efficient algorithms for minimum weighted colouring of some classes of perfect graphs
Discrete Applied Mathematics
Algorithms for weakly triangulated graphs
Discrete Applied Mathematics
Polynomial algorithms for the maximum stable set problem on particular classes of P5-free graphs
Information Processing Letters
Weighted parameters in (P5,&Pmacr;5)-free graphs
Discrete Applied Mathematics
A nice class for the vertex packing problem
GO-II Meeting Proceedings of the second international colloquium on Graphs and optimization
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
Weakly chordal graph algorithms via handles
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
A note on &agr;-redundant vertices in graphs
Discrete Applied Mathematics
A transformation which preserves the clique number
Journal of Combinatorial Theory Series B
Information Processing Letters
Discrete Mathematics
On the stable set problem in special P5-free graphs
Discrete Applied Mathematics
Recognizing weakly triangulated graphs by edge separability
Nordic Journal of Computing
Structure and stability number of chair-, co-P- and gem-free graphs revisited
Information Processing Letters
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
On the structure and stability number of P5- and co-chair-free graphs
Discrete Applied Mathematics - Special issue on stability in graphs and related topics
P5-free augmenting graphs and the maximum stable set problem
Discrete Applied Mathematics - Special issue on stability in graphs and related topics
Some results on maximum stable sets in certain P5-free graphs
Discrete Applied Mathematics - Special issue on stability in graphs and related topics
Polynomial algorithm for finding the largest independent sets in graphs without forks
Discrete Applied Mathematics
Efficient robust algorithms for the maximum weight stable set problem in chair-free graph classes
Information Processing Letters
Independent sets in extensions of 2K2-free graphs
Discrete Applied Mathematics
On the structure of (P5,gem)-free graphs
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
Chordal co-gem-free and (P5,gem)-free graphs have bounded clique-width
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
Stability number of bull- and chair-free graphs revisited
Discrete Applied Mathematics
(P5,diamond)-free graphs revisited: structure and linear time optimization
Discrete Applied Mathematics
On clique separators, nearly chordal graphs, and the maximum weight stable set problem
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
| Hi-index | 0.00 |
Graph decompositions such as decomposition by clique separators and modular decomposition are of crucial importance for designing efficient graph algorithms. Clique separators in graphs were used by Tarjan as a divide-and-conquer approach for solving various problems such as the Maximum Weight Stable Set (MWS) Problem, Coloring and Minimum Fill-in. The basic tool is a decomposition tree of the graph whose leaves have no clique separator (so-called atoms), and the problem can be solved efficiently on the graph if it is efficiently solvable on its atoms. We give new examples where the clique separator decomposition works well for the MWS problem which also improves and extends various recently published results. In particular, we describe the atom structure for some new classes of graphs whose atoms are P5-free (the P5 is the induced path with 5 vertices) and obtain new polynomial time results for MWS.