Abstract
The problem to decide whether the tree-width of a comparability graph is less than k is NP-complete, if k is part of the input. We prove that the tree-width of comparability graphs of interval orders can be determined in linear time and that it equals the path-width of the graph. Our proof is constructive, i.e., we give an explicit path decomposition of the graph.
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S. Arnborg, D.G. Corneil, and A. Proskurowski (1987). Complexity of finding embeddings in a k-tree. SIAM J. Alg. Disc. Meth., vol. 8, No.2, 277–284.
H.L. Bodlaender (1993). A tourist guide through treewidth. Acta Cybernetica, Vol. 11, No. 1–2, Szeged.
H.L. Bodlaender and T. Kloks (1991). Better algorithms for the pathwidth and treewidth of graphs. In Proceedings of the 18th Colloquium on Automata, Languages and Programming, Springer Verlag, Lecture Notes in Computer Sciences, vol. 510, 544–555.
H.L. Bodlaender and R.H. Möhring (1993). The path-width and tree-width of cographs. SIAM J. Discrete Math., vol. 6, 181–188.
H.N. Gabow (1981). A linear-time recognition algorithm for interval dags. Information Processing Letters, vol. 12, No. 1, 20–22.
R. Garbe (1994). Algorithmic Aspects of Interval Orders. Ph.D. Thesis, University of Twente, The Netherlands. To appear in October 1994.
P.C. Gilmore and A.J. Hoffman (1964). A characterization of comparability graphs and of interval graphs. Cand. J. Math., vol. 16, 539–548.
M.C. Golumbic (1980). Algorithmic Graph Theory and Perfect Graphs. Academic Press, New York.
M. Habib and R. H. Möhring (1992). Treewidth of cocomparability graphs and a new order-theoretic parameter. Technical report 336, Technische Universität Berlin. To appear in Order.
K. Jansen and P. Scheffler (1992). Generalized coloring for tree-like graphs. Proceedings of the 18th International Workshop on Graph-Theoretic Concepts in Computer Science, Lecture Notes in Computer Science 657, 50–59.
T. Kloks (1993). Tree-width, Ph.D. Thesis, Utrecht University, The Netherlands.
R.H. Möhring (1993). Triangulating graphs without Asteroidal Triples. Technical report No. 365/1993, Technische Universität Berlin.
C.H. Papadimitriou and M. Yannakakis (1979). Scheduling interval ordered tasks. SIAM J. Computation, 8, 405–409.
A. Proskurowski and M.M. Sysło (1989). Efficient Computations in Tree-Like graphs. In G. Tinhofer, E. Mayr, H. Noltemeier and M. Sysło (eds.), Computational Graph Theory Springer Verlag, Wien New York, 1–15.
N. Robertson and P.D. Seymour (1983). Graph minors. I. Excluding a forest. J. Comb. Theory Series B, vol. 35, 39–61.
N. Robertson and P.D. Seymour (1986). Graph minors. II. Algorithmic aspects of tree-width. J. Algorithms, vol. 7, 309–322.
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© 1995 Springer-Verlag Berlin Heidelberg
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Garbe, R. (1995). Tree-width and path-width of comparability graphs of interval orders. In: Mayr, E.W., Schmidt, G., Tinhofer, G. (eds) Graph-Theoretic Concepts in Computer Science. WG 1994. Lecture Notes in Computer Science, vol 903. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59071-4_35
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DOI: https://doi.org/10.1007/3-540-59071-4_35
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