D. J. Uings, Reflections, The algorithm works in the following way. For each node t ? V (T ) and for each entry M of its table, instead of storing A t (M ), we store A t (M ) = reduce(A t (M )) by using Theorem 3. As each of the operations we use preserves representation by Proposition 2, we obtain that for each node t ? V (T ) and for each possible entry M , A t (M ) represents A t (M ), pp.113-177

Z. Bai, J. Tu, and Y. Shi, Treewidth of treewidth-bounded graphs, Treewidth, pp.173-183

J. Baste, I. Sau, and D. M. Thilikos, Hitting minors on bounded treewidth graphs. II. Single-exponential algorithms, Theoretical Computer Science, vol.814, pp.135-152, 2020.
URL : https://hal.archives-ouvertes.fr/lirmm-02989938

J. Baste and I. Sau, The Role of Planarity in Connectivity Problems Parameterized by Treewidth, Parameterized and Exact Computation, vol.115, pp.63-74, 2014.
URL : https://hal.archives-ouvertes.fr/dumas-00854884

J. Baste, I. Sau, and D. M. Thilikos, Hitting Minors on Bounded Treewidth Graphs. I. General Upper Bounds, SIAM Journal on Discrete Mathematics, vol.34, issue.3, pp.1623-1648, 2020.
URL : https://hal.archives-ouvertes.fr/lirmm-02989938

J. Baste, I. Sau, and D. M. Thilikos, Hitting minors on bounded treewidth graphs. III. Lower bounds, Journal of Computer and System Sciences, vol.109, pp.56-77, 2020.
URL : https://hal.archives-ouvertes.fr/lirmm-02989938

B. Bergougnoux, M. M. Kanté, and O. Kwon, An Optimal XP Algorithm for Hamiltonian Cycle on Graphs of Bounded Clique-Width, Lecture Notes in Computer Science, pp.121-132, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01590820

H. L. Bodlaender, M. Cygan, S. Kratsch, and J. Nederlof, Deterministic single exponential time algorithms for connectivity problems parameterized by treewidth, Information and Computation, vol.243, pp.86-111, 2015.

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.

D. Chatzidimitriou, J. Raymond, I. Sau, and D. M. Thilikos, An $$O(\log \mathrm {OPT})$$ O ( log OPT ) -Approximation for Covering and Packing Minor Models of $$\theta _r$$ ? r, Algorithmica, vol.80, issue.4, pp.1330-1356, 2017.
URL : https://hal.archives-ouvertes.fr/lirmm-01609998

B. Courcelle, The monadic second-order logic of graphs. I. Recognizable sets of finite graphs, Information and Computation, vol.85, issue.1, pp.12-75, 1990.
URL : https://hal.archives-ouvertes.fr/hal-00353765

M. Cygan, F. V. Fomin, ?. Kowalik, D. Lokshtanov, D. Marx et al., Advanced kernelization algorithms, Parameterized Algorithms, pp.285-319, 2015.

M. Cygan, J. Nederlof, M. Pilipczuk, M. Pilipczuk, J. M. Rooij et al., Solving Connectivity Problems Parameterized by Treewidth in Single Exponential Time, 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, pp.150-159, 2011.

R. Diestel, Extremal Graph Theory, Graph Theory, vol.173, pp.173-207, 2017.

R. G. Downey and M. R. Fellows, Parameterized Approximation, Texts in Computer Science, pp.623-644, 2013.

S. Fiorini and A. Herinckx, A Tighter Erd?s-Pósa Function for Long Cycles, Journal of Graph Theory, vol.77, issue.2, pp.111-116, 2013.

F. V. Fomin, D. Lokshtanov, F. Panolan, and S. Saurabh, Efficient Computation of Representative Families with Applications in Parameterized and Exact Algorithms, Journal of the ACM, vol.63, issue.4, pp.1-60, 2016.

R. Impagliazzo, R. Paturi, and F. Zane, Which Problems Have Strongly Exponential Complexity?, Journal of Computer and System Sciences, vol.63, issue.4, pp.512-530, 2001.

T. Kloks, Treewidth, Treewidth. Computations and Approximations, 1994.

D. Lokshtanov, D. Marx, and S. Saurabh, Lower bounds based on the exponential time hypothesis, Bulletin of the EATCS, vol.105, pp.41-72, 2011.

D. Paik, S. M. Reddy, and S. Sahni, Deleting vertices to bound path length, IEEE Transactions on Computers, vol.43, issue.9, pp.1091-1096, 1994.

J. Tu, L. Wu, J. Yuan, and L. Cui, On the vertex cover $$P_3$$ P 3 problem parameterized by treewidth, Journal of Combinatorial Optimization, vol.34, issue.2, pp.414-425, 2016.