B. Anand, M. Changat, S. Klav?ar, and I. Peterin, Convex sets in lexicographic products of graphs. Graphs and Combinatorics, pp.1-8, 2011.

J. Araujo, V. Campos, F. Giroire, N. Nisse, L. Sampaio et al., On the hull number of some graph classes
URL : https://hal.archives-ouvertes.fr/inria-00576581

J. Araujo, V. Campos, F. Giroire, L. Sampaio, and R. Soares, On the hull number of some graph classes, The Sixth European Conference on Combinatorics, Graph Theory and Applications, pp.49-55, 2011.
DOI : 10.1016/j.endm.2011.09.009

URL : https://hal.archives-ouvertes.fr/inria-00576581

J. Araujo, V. Campos, F. Giroire, N. Nisse, L. Sampaio et al., On the hull number of some graph classes, Theoretical Computer Science, vol.475, pp.1-12, 2013.
DOI : 10.1016/j.tcs.2012.12.035

URL : https://hal.archives-ouvertes.fr/inria-00576581

J. Araujo, G. Morel, L. Sampaio, R. Soares, and V. Weber, Hull number: -free graphs and reduction rules, LAGOS'13: Seventh Latin-American Algorithms, Graphs, and Optimization Symposium, pp.171-175, 2016.
DOI : 10.1016/j.endm.2013.10.011

URL : https://hal.archives-ouvertes.fr/hal-00724120

J. Araujo, V. Campos, D. Girão, J. Nogueira, A. Salgueiro et al., Cycle convexity and the tunnel number of links, 2018.

R. T. Araújo, R. M. Sampaio, and J. L. Szwarcfiter, The convexity of induced paths of order three, Electronic Notes in Discrete Mathematics, vol.44, pp.109-114, 2013.
DOI : 10.1016/j.endm.2013.10.017

L. Babel and S. Olariu, On the isomorphism of graphs with few P4s, Proceedings of the 21st International Workshop on Graph-Theoretic Concepts in Computer Science, WG '95, pp.24-36, 1995.
DOI : 10.1007/3-540-60618-1_63

L. Babel and S. Olariu, On the structure of graphs with few P4s, Discrete Applied Mathematics, vol.84, issue.1-3, pp.1-13, 1998.
DOI : 10.1016/S0166-218X(97)90120-7

L. Babel and S. Olariu, On the p-connectedness of graphs ??? a survey, Discrete Applied Mathematics, vol.95, issue.1-3, pp.11-33, 1999.
DOI : 10.1016/S0166-218X(99)00062-1

L. Babel, T. Kloks, J. Kratochvil, D. Kratsch, H. Müller et al., Efficient algorithms for graphs with few P4's, Discrete Mathematics, vol.235, issue.1-3, pp.29-51, 2001.
DOI : 10.1016/S0012-365X(00)00258-2

G. Bacsó and Z. Tuza, Dominating cliques in P5-free graphs, Periodica Mathematica Hungarica, vol.3, issue.4, pp.303-308, 1990.
DOI : 10.1007/BF02352694

P. Balister, B. Bollobás, J. R. Johnson, and M. Walters, Random majority percolation. Random Structures & Algorithms, pp.315-340, 2010.
DOI : 10.1002/rsa.20281

J. Balogh and B. Bollobás, Sharp thresholds in bootstrap percolation Physica A: Statistical Mechanics and its Applications, pp.305-312, 2003.

J. Balogh and G. Pete, Random disease on the square grid Random Structures & Algorithms ISSN 1098-2418. doi: 10.1002/(SICI), 4<409::AID-RSA11>3.0.CO, pp.3-4409, 1998.

J. R. Blair and B. Peyton, An introduction to chordal graphs and clique trees, The IMA Volumes in Mathematics and its Applications, pp.1-29, 1993.
DOI : 10.2172/10145949

H. L. Bodlaender, A partial k-arboretum of graphs with bounded treewidth, Theoretical Computer Science, vol.209, issue.1-2, pp.1-45, 1998.
DOI : 10.1016/S0304-3975(97)00228-4

H. L. Bodlaender, P. G. Drange, M. S. Dregi, F. V. Fomin, D. Lokshtanov et al., A $c^k n$ 5-Approximation Algorithm for Treewidth, SIAM Journal on Computing, vol.45, issue.2, pp.317-378, 2016.
DOI : 10.1137/130947374

URL : http://arxiv.org/pdf/1304.6321.pdf

J. A. Bondy and U. S. Murty, Graph Theory. Graduate Texts in Mathematics, 2008.

C. Bujtás and S. Jaskó, -domination number, Discrete Applied Mathematics, vol.242, 2017.
DOI : 10.1016/j.dam.2017.05.014

J. Cáceres, C. Hernando, M. Mora, I. M. Pelayo, and M. L. Puertas, On the geodetic and the hull numbers in strong product graphs, Computers & Mathematics with Applications, vol.60, issue.11, pp.3020-3031, 2010.
DOI : 10.1016/j.camwa.2010.10.001

G. B. Cagaanan and S. R. Canoy-jr, On the hull sets and hull number of the cartesian product of graphs, Discrete Mathematics, vol.287, issue.1-3, pp.141-144, 2004.
DOI : 10.1016/j.disc.2004.06.014

V. Campos, R. M. Sampaio, A. Silva, and J. L. Szwarcfiter, Graphs with few <mml:math altimg="si1.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:msub><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub></mml:math>???s under the convexity of paths of order three, 11th Cologne/Twente Workshop on Graphs and Combinatorial Optimization, pp.28-39, 2012.
DOI : 10.1016/j.dam.2014.05.005

C. C. Centeno, S. Dantas, M. C. Dourado, D. Rautenbach, and J. L. Szwarcfiter, Convex partitions of graphs induced by paths of order three, Discrete Mathematics & Theoretical Computer Science, vol.12, issue.5, pp.175-184, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00990463

M. Changat and J. Mathew, On triangle path convexity in graphs, Discrete Mathematics, vol.206, issue.1-3, pp.91-95, 1999.
DOI : 10.1016/S0012-365X(98)00394-X

M. Changat, H. M. Mulder, and G. Sierksma, Convexities related to path properties on graphs, Discrete Mathematics, vol.290, issue.2-3, pp.117-131, 2005.
DOI : 10.1016/j.disc.2003.07.014

URL : https://doi.org/10.1016/j.disc.2003.07.014

G. Chartrand, F. Harary, and P. Zhang, On the geodetic number of a graph, Networks, vol.4, issue.1, pp.1-6, 2002.
DOI : 10.1016/0012-365X(73)90116-7

G. Chartrand, C. E. Wall, and P. Zhang, The Convexity Number of a Graph, Graphs and Combinatorics, vol.18, issue.2, pp.209-217, 1007.
DOI : 10.1007/s003730200014

G. Chartrand, C. E. Wall, and P. Zhang, The Convexity Number of a Graph, Graphs and Combinatorics, vol.18, issue.2, pp.209-217, 2002.
DOI : 10.1007/s003730200014

G. Chartrand, J. F. Fink, and P. Zhang, The hull number of an oriented graph, International Journal of Mathematics and Mathematical Sciences, vol.2003, issue.36, pp.2265-2275, 2003.
DOI : 10.1155/S0161171203210577

M. Chellali, O. Favaron, A. Hansberg, and L. Volkmann, k-domination and k-independence in graphs: A survey. Graphs and Combinatorics, pp.1-55, 2012.

X. Chen and V. Chvátal, Problems related to a de Bruijn???Erd??s theorem, Discrete Applied Mathematics, vol.156, issue.11, pp.2101-2108, 2008.
DOI : 10.1016/j.dam.2007.05.036

E. Chiniforooshan and V. Chvátal, A de Bruijn -Erdös theorem and metric spaces, 2009.

M. Chlebík and J. Chlebíková, Approximation hardness of dominating set problems in bounded degree graphs, Information and Computation, vol.206, issue.11, pp.1264-1275, 2008.
DOI : 10.1016/j.ic.2008.07.003

B. Clark, The Heegaard genus of manifolds obtained by surgery on links and knots, International Journal of Mathematics and Mathematical Sciences, vol.3, issue.3, pp.583-589, 1980.
DOI : 10.1155/S0161171280000440

E. M. Coelho, M. C. Dourado, and R. M. Sampaio, Inapproximability Results for Graph Convexity Parameters, pp.97-107, 2014.
DOI : 10.1007/978-3-319-08001-7_9

B. Courcelle and M. Mosbah, Monadic second-order evaluations on tree-decomposable graphs, Theoretical Computer Science, vol.109, issue.1-2, pp.49-82, 1993.
DOI : 10.1016/0304-3975(93)90064-Z

URL : http://www.labri.fr/perso/courcell/Textes1/BC-Mosbah(1993).pdf

I. Dinur and D. Steurer, Analytical approach to parallel repetition, Proceedings of the 46th Annual ACM Symposium on Theory of Computing, STOC '14, pp.624-633, 2014.
DOI : 10.1007/978-3-642-15369-3_54

URL : http://www.cs.cornell.edu/~dsteurer/papers/productgames.pdf

M. C. Dourado, J. G. Gimbel, J. Kratochvíl, F. Protti, and J. L. Szwarcfiter, On the computation of the hull number of a graph, Discrete Mathematics, vol.309, issue.18, pp.5668-5674, 2006.
DOI : 10.1016/j.disc.2008.04.020

M. C. Dourado, F. Protti, D. Rautenbach, and J. L. Szwarcfiter, On the Hull Number of Triangle-Free Graphs, SIAM Journal on Discrete Mathematics, vol.23, issue.4, pp.2163-2172, 2010.
DOI : 10.1137/090751797

M. C. Dourado, F. Protti, and J. L. Szwarcfiter, Complexity results related to monophonic convexity, 2010b. Traces from LAGOS'07 IV Latin American Algorithms, Graphs, and Optimization Symposium Puerto Varas -2007, pp.1268-1274
DOI : 10.1016/j.dam.2009.11.016

URL : https://doi.org/10.1016/j.dam.2009.11.016

M. C. Dourado, D. Rautenbach, V. F. Santos, P. M. Schäfer, J. L. Szwarcfiter et al., An upper bound on the p 3 -radon number, Discrete Mathematics, issue.16, pp.3122433-2437, 2012.

M. C. Dourado, D. Rautenbach, V. F. Santos, P. M. Schäfer, and J. L. Szwarcfiter, On the Carath??odory number of interval and graph convexities, Theoretical Computer Science, vol.510, pp.127-135, 2013.
DOI : 10.1016/j.tcs.2013.09.004

P. A. Dreyer and F. S. Roberts, Irreversible <mml:math altimg="si38.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi>k</mml:mi></mml:math>-threshold processes: Graph-theoretical threshold models of the spread of disease and of opinion, Discrete Applied Mathematics, vol.157, issue.7, pp.1615-1627, 2009.
DOI : 10.1016/j.dam.2008.09.012

P. Duchet, Convex sets in graphs, II. Minimal path convexity, Journal of Combinatorial Theory, Series B, vol.44, issue.3, pp.307-316, 1988.
DOI : 10.1016/0095-8956(88)90039-1

M. G. Everett and S. B. Seidman, The hull number of a graph, Discrete Mathematics, vol.57, issue.3, pp.217-223, 1985.
DOI : 10.1016/0012-365X(85)90174-8

M. Farber and R. E. Jamison, Convexity in Graphs and Hypergraphs, SIAM Journal on Algebraic Discrete Methods, vol.7, issue.3, pp.433-444, 1986.
DOI : 10.1137/0607049

A. Farrugia, Orientable convexity, geodetic and hull numbers in graphs, Discrete Applied Mathematics, vol.148, issue.3, pp.256-262, 2005.
DOI : 10.1016/j.dam.2005.03.002

J. Flum and M. Grohe, Parameterized Complexity Theory. Texts in Theoretical Computer Science. An EATCS Series, 2006.

F. V. Fomin, P. Golovach, and D. M. Thilikos, Contraction obstructions for treewidth, Journal of Combinatorial Theory, Series B, vol.101, issue.5, pp.302-314, 2011.
DOI : 10.1016/j.jctb.2011.02.008

URL : https://doi.org/10.1016/j.jctb.2011.02.008

R. Ganian, Using neighborhood diversity to solve hard problems. CoRR, abs, 1201.

M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, 1979.

M. R. Garey and D. S. Johnson, Computers and Intractability; A Guide to the Theory of NP-Completeness, 1990.

V. Giakoumakis and J. Vanherpe, On extended P4-reducible and extended P4-sparse graphs, Theoretical Computer Science, vol.180, issue.1-2, pp.269-286, 1997.
DOI : 10.1016/S0304-3975(96)00220-4

URL : https://hal.archives-ouvertes.fr/hal-00467644

C. Hernando, T. Jiang, M. Mora, I. M. Pelayo, and C. Seara, On the Steiner, geodetic and hull numbers of graphs, 19th British Combinatorial Conference19th British Combinatorial Conference, pp.139-154, 2005.
DOI : 10.1016/j.disc.2004.08.039

C. Hernando, T. Jiang, M. Mora, I. M. Pelayo, and C. Seara, On the Steiner, geodetic and hull numbers of graphs, British Combinatorial Conference, pp.139-154, 2005.
DOI : 10.1016/j.disc.2004.08.039

M. Hujter and Z. Tuza, Precoloring extension. ii. graphs classes related to bipartite graphs, ACTA MATH- EMATICA UNIVERSITATIS COMENIANAE, vol.62, issue.1, pp.1-11, 1993.

B. Jamison and S. Olariu, A tree representation for P4-sparse graphs, Discrete Applied Mathematics, vol.35, issue.2, pp.115-129, 1992.
DOI : 10.1016/0166-218X(92)90036-A

URL : https://doi.org/10.1016/0166-218x(92)90036-a

R. E. Jamison, A perspective on abstract convexity: Classifying alignments by varieties, Convexity and Related CombinatorialGeometry, 1982.

R. M. Karp, Reducibility Among Combinatorial Problems, Complexity of Computer Computations, pp.85-103, 1972.
DOI : 10.1007/978-1-4684-2001-2_9

M. Lampis, Algorithmic Meta-theorems for Restrictions of Treewidth, Algorithmica, vol.4, issue.3, pp.19-37
DOI : 10.1287/moor.8.4.538

C. Lekkeikerker and J. Boland, Representation of a finite graph by a set of intervals on the real line, Fundamenta Mathematicae, vol.51, issue.1, pp.45-64, 1962.
DOI : 10.4064/fm-51-1-45-64

J. Liu and H. Zhou, Dominating subgraphs in graphs with some forbidden structures, Discrete Mathematics, vol.135, issue.1-3, pp.1-3163, 1994.
DOI : 10.1016/0012-365X(93)E0111-G

R. M. Mcconnell and J. P. Spinrad, Modular decomposition and transitive orientation, Discrete Mathematics, vol.201, issue.1-3, pp.189-241, 1999.
DOI : 10.1016/S0012-365X(98)00319-7

A. Nayak, J. Ren, and N. Santoro, An improved testing scheme for catastrophic fault patterns, Information Processing Letters, vol.73, issue.5-6, pp.199-206, 2000.
DOI : 10.1016/S0020-0190(00)00012-0

E. M. Paluga and S. R. Canoy-jr, Monophonic numbers of the join and composition of connected graphs, Discrete Mathematics, vol.307, issue.9-10, pp.1146-1154, 2007.
DOI : 10.1016/j.disc.2006.08.002

I. Pelayo, Geodesic Convexity in Graphs. SpringerBriefs in Mathematics, 2013.

D. Peleg, Local majorities, coalitions and monopolies in graphs: a review, Theoretical Computer Science, vol.282, issue.2, pp.231-257, 2002.
DOI : 10.1016/S0304-3975(01)00055-X

I. Peterin, The pre-hull number and lexicographic product365X. Special Issue: The Sixth Cracow Conference on Graph Theory, Discrete Mathematics, issue.14, pp.3122153-2157, 2010.
DOI : 10.1016/j.disc.2011.08.031

URL : https://doi.org/10.1016/j.disc.2011.08.031

I. F. Ramos, V. F. Santos, and J. L. Szwarcfiter, Complexity aspects of the computation of the rank of a graph, Discrete Mathematics & Theoretical Computer Science, vol.16, issue.2, pp.73-86, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01185615

R. T. Rockafellar, Convex analysis. Princeton Mathematical Series, 1970.

M. Tedder, D. G. Corneil, M. Habib, and C. Paul, Simpler Linear-Time Modular Decomposition Via Recursive Factorizing Permutations, Proceedings of the 35th International Colloquium on Automata, Languages and Programming (ICALP), pp.634-645, 2008.
DOI : 10.4153/CJM-1971-016-5

URL : http://www.cs.utoronto.ca/~mtedder/TedderModular.pdf

J. Varlet, Convexity in tournaments, Bull. Soc. R. Sci.Lì ege, vol.45, pp.570-586, 1976.

S. Wasserman and K. Faust, Social network analysis: Methods and applications, 1994.
DOI : 10.1017/CBO9780511815478