N. R. Aravind, S. Kalyanasundaram, and A. Kare, On Structural Parameterizations of the Matching Cut Problem, Proc. of the 11th International Conference on Combinatorial Optimization and Applications (COCOA), volume 10628 of LNCS, pp.475-482, 2017.

A. Ban and N. Linial, Internal partitions of regular graphs, Journal of Graph Theory, vol.83, issue.1, pp.5-18, 2016.

L. Hans, R. G. Bodlaender, M. R. Downey, D. Fellows, and . Hermelin, On problems without polynomial kernels, Journal of Computer and System Sciences, vol.75, issue.8, pp.423-434, 2009.

L. Hans, . Bodlaender, M. P. Bart, S. Jansen, and . Kratsch, Cross-Composition: A New Technique for Kernelization Lower Bounds, Proc. of the 28th International Symposium on Theoretical Aspects of Computer Science (STACS), vol.9, pp.165-176, 2011.

P. S. Bonsma, The complexity of the matching-cut problem for planar graphs and other graph classes, Journal of Graph Theory, vol.62, issue.2, pp.109-126, 2009.

A. Boral, M. Cygan, T. Kociumaka, and M. Pilipczuk, A fast branching algorithm for cluster vertex deletion. Theory of Computing Systems, vol.58, pp.357-376, 2016.

V. Chvátal, Recognizing decomposable graphs, Journal of Graph Theory, vol.8, issue.1, pp.51-53, 1984.

B. Courcelle, The monadic second-order logic of graphs. I. Recognizable sets of finite graphs. Information and computation, vol.85, pp.12-75, 1990.
URL : https://hal.archives-ouvertes.fr/hal-00353765

M. Cygan, V. Fedor, L. Fomin, D. Kowalik, D. Lokshtanov et al., Marcin Pilipczuk, Michal Pilipczuk, and Saket Saurabh. Parameterized Algorithms, 2015.

M. Devos, , 2009.

, Graph Theory, vol.173, 2010.

R. G. Downey and M. R. Fellows, Fundamentals of Parameterized Complexity. Texts in Computer Science, 2013.

V. Fedor, D. Fomin, S. Lokshtanov, M. Saurabh, and . Zehavi, Kernelization: Theory of Parameterized Preprocessing, 2019.

L. Fortnow and R. Santhanam, Infeasibility of instance compression and succinct PCPs for NP, Journal of Computer and System Sciences, vol.77, issue.1, pp.91-106, 2011.

L. Ron and . Graham, On primitive graphs and optimal vertex assignments, Annals of the New York academy of sciences, vol.175, issue.1, pp.170-186, 1970.

R. Impagliazzo and R. Paturi, On the complexity of k-SAT, Journal of Computer and System Sciences, vol.62, issue.2, pp.367-375, 2001.

A. Kaneko, On decomposition of triangle-free graphs under degree constraints, Journal of Graph Theory, vol.27, issue.1, pp.7-9, 1998.

C. Komusiewicz, D. Kratsch, . Van-bang, and . Le, Matching Cut: Kernelization, Single-Exponential Time FPT, and Exact Exponential Algorithms, Proc. of the 13th International Symposium on Parameterized and Exact Computation (IPEC), volume 115 of LIPIcs, vol.19, pp.1-19, 2018.

D. Kratsch and . Van-bang-le, Algorithms solving the matching cut problem, Theoretical Computer Science, vol.609, pp.328-335, 2016.

H. Le and . Van-bang-le, On the Complexity of Matching Cut in Graphs of Fixed Diameter, Proc. of the 27th International Symposium on Algorithms and Computation (ISAAC), vol.64, 2016.

B. Van-bang-le and . Randerath, On stable cutsets in line graphs, Theoretical Computer Science, vol.301, issue.1-3, pp.463-475, 2003.

J. Ma and T. Yang, Decomposing C4-free graphs under degree constraints, Journal of Graph Theory, vol.90, issue.1, pp.13-23, 2019.

D. Marx, O. Barry, I. Sullivan, and . Razgon, Treewidth Reduction for Constrained Separation and Bipartization Problems, Proc. of the 27th International Symposium on Theoretical Aspects of Computer Science, (STACS), volume 5 of LIPIcs, pp.561-572, 2010.
URL : https://hal.archives-ouvertes.fr/inria-00455767

M. Augustine and . Moshi, Matching cutsets in graphs, Journal of Graph Theory, vol.13, issue.5, pp.527-536, 1989.

M. Patrignani and M. Pizzonia, The complexity of the matching-cut problem, Proc. of the 27th International Workshop on Graph-Theoretic Concepts in Computer Science (WG), vol.2204, pp.284-295, 2001.