Abstract
We show that three subclasses of bounded treewidth graphs are well-quasi-ordered by refinements of the minor order. Specifically, we prove that graphs with bounded feedback-vertex-set are well-quasi-ordered by the topological-minor order, graphs with bounded vertex-covers are well-quasi-ordered by the subgraph order, and graphs with bounded circumference are well-quasi-ordered by the induced-minor order. Our results give an algorithm for recognizing any graph family in these classes which is closed under the corresponding minor order refinement.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Arnborg, S.: Efficient algorithms for combinatorial problems on graphs with bounded decomposability. A survey. BIT Numerical Mathematics 25(1), 2–23 (1985)
Arnborg, S., Proskurowski, A.: Linear time algorithms for NP-hard problems restricted to partial k-trees. Discrete Applied Mathematics 23, 11–24 (1989)
Bodlaender, H.L., Fellows, M.R., Hallett, M.T.: Beyond NP-completeness for problems of bounded width: Hardness for the W-hierarchy. In: Proceedings of the 26th annual ACM Symposium on Theory of Computing (STOC), pp. 449–458 (1994)
Corneil, D.G., Keil, J.M.: A dynamic programming approach to the dominating set problem on k-trees. SIAM Journal on Algebraic and Discrete Methods 8(4), 535–543 (1987)
Courcelle, B.: The monadic second-order logic of graphs I. Recognizable sets of finite graphs. Information and Computation 85(1), 12–75 (1990)
Ding, G.: Subgraphs and well-quasi-ordering. Journal of Graph Theory 16(5), 489–502 (1992)
Downey, R., Fellows, M.: Parameterized Complexity. Springer, Heidelberg (1999)
Fellows, M.R., Langston, M.A.: Fast self-reduction algorithms for combinatorial problems of VLSI design. In: Proc. of the 3rd Aegean Workshop On Computing (AWOC), pp. 278–287 (1988)
Fellows, M.R., Langston, M.A.: On well-paritial-order theory and its application to combinatorial problems of VLSI design. SIAM Journal on Discrete Mathematics 5 (1992)
Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer, Heidelberg (2006)
Kruskal, J.B.: Well-quasi-ordering, the tree theorem, and Vazsonyi’s conjecture. Transactions of the American Mathematical Society 95, 210–225 (1960)
Menger, K.: Zur allgemeinen kurventheorie. Fundamenta Mathematicae 10, 96–115 (1927)
Nash-Williams, C.S.J.A.: On well-quasi-ordering finite trees. Mathematical Proceedings of the Cambridge Philosophical Society 59(4), 833–835 (1963)
Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford University Press, Oxford (2006)
Thomas, R.: Well-quasi-ordering infinite graphs with forbidden finite planar minor. Transactions of the American Mathematical Society 312(1), 67–76 (1990)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fellows, M.R., Hermelin, D., Rosamond, F.A. (2009). Well-Quasi-Orders in Subclasses of Bounded Treewidth Graphs. In: Chen, J., Fomin, F.V. (eds) Parameterized and Exact Computation. IWPEC 2009. Lecture Notes in Computer Science, vol 5917. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11269-0_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-11269-0_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11268-3
Online ISBN: 978-3-642-11269-0
eBook Packages: Computer ScienceComputer Science (R0)