, If D is a minimal dominating set of G containing A, then D \ A ? {x 1 , ¬x 1 , . . . , x n , ¬x n } and it contains at most one literal for each variable

, Notice that Priv(A, v) = {u}. If y Cj belongs to D for some j ? {1, vol.15

. Hence, .. .. C1, }. Cm, . Besides, and .. {1, m}, D contains at most one of x i and ¬x i , as otherwise Priv(D, neg xi ) would be empty

A. Eralp-abdurrahim, The enumeration of maximal cliques of large graphs, SIAM Journal on Computing, vol.2, issue.1, pp.1-6, 1973.

J. M. Barnard, Substructure searching methods: Old and new, Journal of Chemical Information and Computer Sciences, vol.33, issue.4, pp.532-538, 1993.

J. Byskov, Enumerating maximal independent sets with applications to graph colouring, Operations Research Letters, vol.32, issue.6, pp.547-556, 2004.

B. Courcelle, Linear delay enumeration and monadic second-order logic, Discrete Applied Mathematics, vol.157, issue.12, pp.2675-2700, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00333846

P. Damaschke, Parameterized Enumeration, Transversals, and Imperfect Phylogeny Reconstruction, Parameterized and Exact Computation, pp.1-12, 2004.

T. Eiter and G. Gottlob, Hypergraph transversal computation and related problems in logic and AI, European Workshop on Logics in Artificial Intelligence, pp.549-564

. Springer, , 2002.

T. Eiter, G. Gottlob, and K. Makino, New results on monotone dualization and generating hypergraph transversals, SIAM Journal on Computing, vol.32, issue.2, pp.514-537, 2003.

T. Eiter, K. Makino, and G. Gottlob, Computational aspects of monotone dualization: A brief survey, Discrete Applied Mathematics, vol.156, issue.11, pp.2035-2049, 2008.

L. Michael, L. Fredman, and . Khachiyan, On the complexity of dualization of monotone disjunctive normal forms, Journal of Algorithms, vol.21, issue.3, pp.618-628, 1996.

P. A. Golovach, P. Heggernes, D. Mamadou-moustapha-kanté, . Kratsch, H. Sigve et al., Output-Polynomial Enumeration on Graphs of Bounded (Local) Linear MIM-Width, Algorithmica, vol.80, issue.2, pp.714-741, 2018.
URL : https://hal.archives-ouvertes.fr/hal-02083480

P. A. Golovach, P. Heggernes, M. Mamadou, D. Kanté, Y. Kratsch et al., Enumerating minimal dominating sets in chordal bipartite graphs, Special Issue: Sixth Workshop on Graph Classes, Optimization, and Width Parameters, vol.199, pp.30-36, 2013.
URL : https://hal.archives-ouvertes.fr/hal-02083515

P. A. Golovach, P. Heggernes, D. Kratsch, and Y. Villanger, An Incremental Polynomial Time Algorithm to Enumerate All Minimal Edge Dominating Sets, Algorithmica, vol.72, issue.3, pp.836-859, 2015.

J. A. Grochow and M. Kellis, Network motif discovery using subgraph enumeration and symmetry-breaking, Annual International Conference on Research in Computational Molecular Biology, pp.92-106, 2007.

M. Hujtera and Z. Tuza, The Number of Maximal Independent Sets in Triangle-Free Graphs, SIAM Journal on Discrete Mathematics, vol.6, issue.2, pp.284-288, 1993.

V. Mamadou-moustapha-kanté, A. Limouzy, L. Mary, and . Nourine, Enumeration of minimal dominating sets and variants, International Symposium on Fundamentals of Computation Theory, pp.298-309, 2011.

V. Mamadou-moustapha-kanté, A. Limouzy, L. Mary, and . Nourine, On the neighbourhood helly of some graph classes and applications to the enumeration of minimal dominating sets, International Symposium on Algorithms and Computation, pp.289-298

. Springer, , 2012.

V. Mamadou-moustapha-kanté, A. Limouzy, L. Mary, and . Nourine, On the Enumeration of Minimal Dominating Sets and Related Notions, SIAM Journal on Discrete Mathematics, vol.28, issue.4, pp.1916-1929, 2014.

V. Mamadou-moustapha-kanté, A. Limouzy, L. Mary, T. Nourine, and . Uno, On the enumeration and counting of minimal dominating sets in interval and permutation graphs, International Symposium on Algorithms and Computation, pp.339-349, 2013.

V. Mamadou-moustapha-kanté, A. Limouzy, L. Mary, T. Nourine, and . Uno, A polynomial delay algorithm for enumerating minimal dominating sets in chordal graphs, In International Workshop on Graph-Theoretic Concepts in Computer Science, pp.138-153, 2015.

M. Mamadou, L. Kanté, and . Nourine, Minimal Dominating Set Enumeration, Encyclopedia of Algorithms, pp.1-5, 2014.

M. P. Marcus, Derivation of Maximal Compatibles Using Boolean Algebra, IBM Journal of Research and Development, vol.8, issue.5, pp.537-538, 1964.

A. Marino, An Application: Biological Graph Analysis, Analysis and Enumeration: Algorithms for Biological Graphs, pp.37-44, 2015.

A. Marino, Enumeration Algorithms, Analysis and Enumeration: Algorithms for Biological Graphs, pp.13-35, 2015.

M. C. Paull and S. H. Unger, Minimizing the Number of States in Incompletely Specified Sequential Switching Functions, IRE Transactions on Electronic Computers, EC, vol.8, issue.3, pp.356-367, 1959.

Y. Strozecki, Enumeration complexity and matroid decomposition, 2010.

R. Tarjan, Enumeration of the elementary circuits of a directed graph, SIAM Journal on Computing, vol.2, issue.3, pp.211-216, 1973.

J. C. Tiernan, An efficient search algorithm to find the elementary circuits of a graph, Communications of the ACM, vol.13, issue.12, pp.722-726, 1970.

K. Wasa, Enumeration of enumeration algorithms, 2016.

X. Yan, P. S. Yu, and J. Han, Substructure similarity search in graph databases, Proceedings of the 2005 ACM SIGMOD international conference on Management of data, pp.766-777, 2005.