Abstract
It is known to be NP-hard to decide whether a graph can be made chordal by the deletion of k vertices. Here we present a uniformly polynomial-time algorithm for the problem: the running time is f(k) n α for some constant α not depending on k and some f depending only on k. For large values of n, such an algorithm is much better than trying all the O(n k) possibilities. Therefore, the chordal deletion problem parameterized by the number k of vertices to be deleted is fixed-parameter tractable. This answers an open question of Cai [2].
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References
Cai, L.: Fixed-parameter tractability of graph modification problems for hereditary properties. Inform. Process. Lett. 58(4), 171–176 (1996)
Cai, L.: Parameterized complexity of vertex colouring. Discrete Appl. Math. 127, 415–429 (2003)
Downey, R.G., Fellows, M.R.: Parameterized complexity. Springer, Heidelberg (1999)
Golumbic, M.C.: Algorithmic graph theory and perfect graphs. Academic Press, New York (1980)
Kaplan, H., Shamir, R., Tarjan, R.E.: Tractability of parameterized completion problems on chordal, strongly chordal, and proper interval graphs. SIAM J. Comput. 28(5), 1906–1922 (1999)
Lewis, J.M., Yannakakis, M.: The node-deletion problem for hereditary properties is NP-complete. J. Comput. System Sci. 20(2), 219–230 (1980)
Natanzon, A., Shamir, R., Sharan, R.: Complexity classification of some edge modification problems. Discrete Appl. Math. 113(1), 109–128 (2001)
Reed, B., Smith, K., Vetta, A.: Finding odd cycle transversals. Operations Research Letters 32(4), 299–301 (2004)
Rose, D.J., Tarjan, R.E., Lueker, G.S.: Algorithmic aspects of vertex elimination on graphs. SIAM J. Comput. 5(2), 266–283 (1976)
Yannakakis, M.: Computing the minimum fill-in is NP-complete. SIAM J. Algebraic Discrete Methods 2(1), 77–79 (1981)
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© 2006 Springer-Verlag Berlin Heidelberg
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Marx, D. (2006). Chordal Deletion Is Fixed-Parameter Tractable. In: Fomin, F.V. (eds) Graph-Theoretic Concepts in Computer Science. WG 2006. Lecture Notes in Computer Science, vol 4271. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11917496_4
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DOI: https://doi.org/10.1007/11917496_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-48381-6
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