About recognizing (&agr; &bgr;) classes of polar graphs
Discrete Mathematics
The weighted perfect domination problem
Information Processing Letters
Computing a maximum cardinality matching in a bipartite graph in time On1.5m/logn
Information Processing Letters
Easy problems for tree-decomposable graphs
Journal of Algorithms
Information Processing Letters
Regular codes in regular graphs are difficult
Discrete Mathematics
Clique partitions, graph compression and speeding-up algorithms
Journal of Computer and System Sciences
Weighted independent perfect domination on cocomparability graphs
Discrete Applied Mathematics
A wide-range efficient algorithm for minimal triangulation
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Coloring the Maximal Cliques of Graphs
SIAM Journal on Discrete Mathematics
Graph Theory With Applications
Graph Theory With Applications
Discrete Applied Mathematics
Discrete Applied Mathematics
A wide-range algorithm for minimal triangulation from an arbitrary ordering
Journal of Algorithms
A forbidden subgraph characterization of line-polar bipartite graphs
Discrete Applied Mathematics
Recognizing line-polar bipartite graphs in time O(n)
Discrete Applied Mathematics
Recognizing polar planar graphs using new results for monopolarity
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Polar permutation graphs are polynomial-time recognisable
European Journal of Combinatorics
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A graph G=(V,E) is a unipolar graph if there exists a partition V=V"1@?V"2 such that V"1 is a clique and V"2 induces the disjoint union of cliques. The complement-closed class of generalized split graphs contains those graphs G such that either Gor the complement of G is unipolar. Generalized split graphs are a large subclass of perfect graphs. In fact, it has been shown that almost all C"5-free (and hence, almost all perfect graphs) are generalized split graphs. In this paper, we present a recognition algorithm for unipolar graphs that utilizes a minimal triangulation of the given graph, and produces a partition when one exists. Our algorithm has running time O(nm+nm"F), where m"F is the number of edges added in a minimal triangulation of the given graph. Generalized split graphs can be recognized via this algorithm in O(n^3) time. We give algorithms on unipolar graphs for finding a maximum independent set and a minimum clique cover in O(n+m) time, and for finding a maximum clique and a minimum proper coloring in O(n^2^.^5/logn) time, when a unipolar partition is given. These algorithms yield algorithms for the four optimization problems on generalized split graphs that have the same worst-case time bounds. We also report that the perfect code problem is NP-complete for chordal unipolar graphs.