Abstract
Using the specific structure of the minimal separators of AT-free graphs, we give a polynomial time algorithm that computes a triangulation whose width is no more than twice the treewidth of the input graph.
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References
S. Arnborg, D.G. Corneil, and A. Proskurowski. Complexity of finding embeddings in a k-tree. SIAM J. on Algebraic and Discrete Methods, 8:277–284, 1987.
H. Bodlaender, J.R. Gilbert, H. Hafsteinsson, and T. Kloks. Approximating tree-width, pathwidth, and minimum elimination tree height. J. of Algorithms, 18:238–255, 1995.
V. Bouchitté and I. Todinca. Minimal triangulations for graphs with “few” minimal separators. In Proceedings 6th Annual European Symposium on Algorithms (ESA’98), volume 1461 of Lecture Notes in Computer Science, pages 344–355. Springer-Verlag, 1998.
V. Bouchitté and I. Todinca. Treewidth and minimum fill-in of weakly triangulated graphs. In Proceedings 16th Symposium on Theoretical Aspects of Computer Science (STACS’99), volume 1563 of Lecture Notes in Computer Science, pages 197–206. Springer-Verlag, 1999.
V. Bouchitté and I. Todinca. Listing all potential maximal cliques of a graph. In Proceedings 17th Annual Symposium on Theoretical Aspects of Computer Science (STACS 2000), volume 1770 of Lecture Notes in Computer Science, pages 503–515. Springer-Verlag, 2000.
H. Broersma, T. Kloks, D. Kratsch, and H. Müller. A generalization of AT-free graphs and a generic algorithm for solving triangulation problems. In Workshop on Graphs WG’98, volume 1517 of Lecture Notes in Computer Science, pages 88–99. Springer-Verlag, 1998.
M. C. Golumbic. Algorithmic Graph Theory and Perfect Graphs. Academic Press, New York, 1980.
T. Kloks, D. Kratsch, and H. Müller. Approximating the bandwidth for asteroidal triple-free graphs. Journal of Algorithms, 32:41–57, 1999.
T. Kloks, D. Kratsch, and J. Spinrad. On treewidth and minimum fill-in of asteroidal triple-free graphs. Theoretical Computer Science, 175:309–335, 1997.
A. Parra and P. Scheffler. Characterizations and algorithmic applications of chordal graph embeddings. Discrete Appl. Math., 79(1-3):171–188, 1997.
N. Robertson and P. Seymour. Graphs minors. II. Algorithmic aspects of tree-width. J. of Algorithms, 7:309–322, 1986.
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Bouchitté, V., Todinca, I. (2000). Approximating the Treewidth of AT-Free Graphs. In: Brandes, U., Wagner, D. (eds) Graph-Theoretic Concepts in Computer Science. WG 2000. Lecture Notes in Computer Science, vol 1928. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-40064-8_7
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DOI: https://doi.org/10.1007/3-540-40064-8_7
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