On generating all maximal independent sets
Information Processing Letters
An incremental concept formation approach for learning from databases
Theoretical Computer Science - Special issue on formal methods in databases and software engineering
Reverse search for enumeration
Discrete Applied Mathematics - Special volume: first international colloquium on graphs and optimization (GOI), 1992
A Survey of Combinatorial Gray Codes
SIAM Review
Linear-time transitive orientation
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
A fast algorithm for building lattices
Information Processing Letters
Chordal Graphs and Their Clique Graphs
WG '95 Proceedings of the 21st International Workshop on Graph-Theoretic Concepts in Computer Science
Consensus algorithms for the generation of all maximal bicliques
Discrete Applied Mathematics - The fourth international colloquium on graphs and optimisation (GO-IV)
Generating bicliques of a graph in lexicographic order
Theoretical Computer Science
Linear-time counting algorithms for independent sets in chordal graphs
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
A generic algorithm for generating closed sets of a binary relation
ICFCA'05 Proceedings of the Third international conference on Formal Concept Analysis
Finding maximum edge bicliques in convex bipartite graphs
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Termination of multipartite graph series arising from complex network modelling
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part I
Enumeration of minimal dominating sets and variants
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
About the enumeration algorithms of closed sets
ICFCA'10 Proceedings of the 8th international conference on Formal Concept Analysis
A parameterizable enumeration algorithm for sequence mining
Theoretical Computer Science
Cliques in odd-minor-free graphs
CATS '12 Proceedings of the Eighteenth Computing: The Australasian Theory Symposium - Volume 128
Enumerating maximal bicliques in bipartite graphs with favorable degree sequences
Information Processing Letters
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We present a general framework to study enumeration algorithms for maximal cliques and maximal bicliques of a graph. Given a graph G, we introduce the notion of the transition graph T(G) whose vertices are maximal cliques of G and arcs are transitions between cliques. We show that T(G) is a strongly connected graph and characterize a rooted cover tree of T(G) which appears implicitly in [D.S. Johnson, M. Yannakakis, C.H. Papadimitriou, On generating all maximal independent sets, Information Processing Letters 27 (1988) 119-123; S. Tsukiyama, M. Ide, M. Aiyoshi, I. Shirawaka, A new algorithm for generating all the independent sets, SIAM Journal on Computing 6 (1977) 505-517]. When G is a bipartite graph, we show that the Galois lattice of G is a partial graph of T(G) and we deduce that algorithms based on the Galois lattice are a particular search of T(G). Moreover, we show that algorithms in [G. Alexe, S. Alexe, Y. Crama, S. Foldes, P.L. Hammer, B. Simeone, Consensus algorithms for the generation of all maximal bicliques, Discrete Applied Mathematics 145 (1) (2004) 11-21; L. Nourine, O. Raynaud, A fast algorithm for building lattices, Information Processing Letters 71 (1999) 199-204] generate maximal bicliques of a bipartite graph in O(n^2) per maximal biclique, where n is the number of vertices in G. Finally, we show that under some specific numbering, the transition graph T(G) has a hamiltonian path for chordal and comparability graphs.