On diameters and radii of bridged graphs
Discrete Mathematics
A tree representation for P4-sparse graphs
Discrete Applied Mathematics
Handle-rewriting hypergraph grammars
Journal of Computer and System Sciences
A decomposition for a class of &parl0;P5,P5&parr0;- free graphs
Discrete Mathematics
Discrete Mathematics
Polynomial algorithms for the maximum stable set problem on particular classes of P5-free graphs
Information Processing Letters
Proceedings of an international symposium on Graphs and combinatorics
Weighted parameters in (P5,&Pmacr;5)-free graphs
Discrete Applied Mathematics
Graph classes: a survey
Modular decomposition and transitive orientation
Discrete Mathematics - Special issue on partial ordered sets
Upper bounds to the clique width of graphs
Discrete Applied Mathematics
A note on &agr;-redundant vertices in graphs
Discrete Applied Mathematics
Efficient and practical algorithms for sequential modular decomposition
Journal of Algorithms
Discrete Mathematics
New Graph Classes of Bounded Clique-Width
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
A New Linear Algorithm for Modular Decomposition
CAAP '94 Proceedings of the 19th International Colloquium on Trees in Algebra and Programming
Structure and stability number of chair-, co-P- and gem-free graphs revisited
Information Processing Letters
On variations of P4-sparse graphs
Discrete Applied Mathematics
Some results on maximum stable sets in certain P5-free graphs
Discrete Applied Mathematics - Special issue on stability in graphs and related topics
New Graph Classes of Bounded Clique-Width
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
Independent sets in extensions of 2K2-free graphs
Discrete Applied Mathematics
New applications of clique separator decomposition for the Maximum Weight Stable Set problem
Theoretical Computer Science
Maximum independent sets in subclasses of P5-free graphs
Information Processing Letters
Independent sets in extensions of 2K2-free graphs
Discrete Applied Mathematics
First-Fit coloring of {P5,K4-e}-free graphs
Discrete Applied Mathematics
Maximum Weight Independent Sets in hole- and co-chair-free graphs
Information Processing Letters
Clique separator decomposition of hole-free and diamond-free graphs and algorithmic consequences
Discrete Applied Mathematics
Clique-width for four-vertex forbidden subgraphs
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
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
Maximum weight independent sets in hole- and dart-free graphs
Discrete Applied Mathematics
Maximum weight independent sets in (P6,co-banner)-free graphs
Information Processing Letters
On atomic structure of P5-free subclasses and Maximum Weight Independent Set problem
Theoretical Computer Science
Hi-index | 0.01 |
We give a O(nm) time algorithm for the maximum weight stable set (MWS) problem on P5-and co-chair-free graphs without recognizing whether the (arbitrary) input graph is P5- and co-chair-free. This algorithm is based on the fact that prime P5- and co-chair-free graphs containing 2K2 are matched co-bipartite graphs and thus have very simple structure, and for 2K2-free graphs, there is a polynomial time algorithm for the MWS problem due to a result of Farber saying that 2K2-free graphs contain at most O(n2) maximal stable sets. A similar argument can be used for (P5,co-P)-free graphs; their prime graphs are 2K2-free. Moreover, we give a complete classification of (P5,co-chair,H)-free graphs with respect to their clique width when H is a one-vertex P4 extension; this extends the characterization of (P5,P'5,co-chair)-free graphs called semi-P4-sparse by Fouquet and Giakoumakis. For H being a house, P, bull or gem, the class of (P5,co-chair,H)-free graphs has bounded clique width and very simple structure whereas for the other four cases, namely H being a co-gem, chair, co-P or C5, the class has unbounded clique width due to a result of Makowsky and Rotics. Bounded clique width implies linear time algorithms for all algorithmic problems expressible in LinEMSOL--a variant of Monadic Second Order Logic including the MWS Problem.