Abstract
We give a polynomial time algorithm to compute a minimum (weight) feedback vertex set for AT-free graphs, and extending this approach we obtain a polynomial time algorithm for graphs of bounded asteroidal number.
We also present an O(nm 2) algorithm to compute a longest induced path in AT-free graphs.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Bafna, V., Berman, P., Fujito, T.: A 2-approximation algorithm for the undirected feedback vertex set problem. SIAM Journal on Discrete Mathematics 12, 289–297 (1999)
Bodlaender, H., Thilikos, D.: Treewidth for graphs with small chordality. Discrete Applied Mathematics 79, 45–61 (1997)
Brandstädt, A., Kratsch, D.: On domination problems for permutation and other graphs. Theoretical Computer Science 54, 181–198 (1987)
Brandstädt, A., Lozin, V.V.: On the linear structure and clique width of bipartite permutation graphs, RRR-29-2001, Rutgers University
Broersma, H.J., Huck, A., Kloks, T., Koppius, O., Kratsch, D., Müller, H., Tuinstra, H.: Degreepreserving trees. Networks 35, 26–39 (2000)
Broersma, H.J., Kloks, T., Kratsch, D., Müller, H.: Independent sets in asteroidal triple-free graphs. SIAM Journal on Discrete Mathematics 12, 276–287 (1999)
Broersma, H.J., Kloks, T., Kratsch, D., Müller, H.: A generalization ofAT-free graphs and a generic algorithm for solving triangulation problems. Algorithmica 32, 594–610 (2002)
Corneil, D.G., Olariu, S., Stewart, L.: Asteroidal triple-free graphs. SIAM Journal on Discrete Mathematics 10, 399–430 (1997)
Courcelle, B., Makowsky, J.A., Rotics, U.: Linear time solvable optimization problems on graphs of bounded clique-width. Theory of Computing Systems 33, 125–150 (2000)
Downey, R.G., Fellows, M.R.: Parameterized complexity. Springer, Heidelberg (1997)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A guide to the Theory of NP-completeness. Freeman, NewYork (1979)
Gavril, F.: Algorithms for maximum weight induced paths. Information Processing Letters 81, 203–208 (2002)
Kloks, K., Kratsch, D., Müller, H.: Asteroidal sets in graphs. In: Möhring, R.H. (ed.) WG 1997. LNCS, vol. 1335, pp. 229–241. Springer, Heidelberg (1997)
Kleinberg, J., Kumar, A.: Wavelength conversion in optical networks. Journal of Algorithms 38, 25–50 (2001)
Köhler, E.: Graphs without asteroidal triples, PhD thesis, TU Berlin (1999), ftp://ftp.math.tu-berlin.de/pub/combi/ekoehler/diss
Liang, D.Y.: On the feedback vertex set problem in permutation graphs. Information Processing Letters 52, 123–129 (1994)
Liang, D.Y., Chang, M.S.: Minimum feedback vertex sets in cocomparability graphs and convex bipartite graphs. Acta Informatica 34, 337–346 (1997)
Lu, C.L., Tang, C.Y.: A linear-time algorithm for the weighted feedback vertex problem on interval graphs. Information Processing Letters 61, 107–111 (1997)
Spinrad, J.: Efficient graph representations, American Mathematical Society, Fields Institute Monograph Series 19 (2003)
Tarjan, R.: Depth-first search and linear graph algorithms. SIAM Journal on Computing 1, 146–160 (1972)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kratsch, D., Müller, H., Todinca, I. (2003). Feedback Vertex Set and Longest Induced Path on AT-Free Graphs. In: Bodlaender, H.L. (eds) Graph-Theoretic Concepts in Computer Science. WG 2003. Lecture Notes in Computer Science, vol 2880. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39890-5_27
Download citation
DOI: https://doi.org/10.1007/978-3-540-39890-5_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20452-7
Online ISBN: 978-3-540-39890-5
eBook Packages: Springer Book Archive