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Journal of Discrete Mathematics
Volume 2013 (2013), Article ID 692645, 4 pages
Another Note on Dilworth's Decomposition Theorem
Erasmus University Rotterdam, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands
Received 8 June 2012; Accepted 9 November 2012
Academic Editor: Stefan Richter
Copyright © 2013 Wim Pijls and Rob Potharst. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- R. P. Dilworth, “A decomposition theorem for partially ordered sets,” Annals of Mathematics, vol. 51, pp. 161–166, 1951.
- D. R. Fulkerson, “Note on Dilworth's decomposition theorem for partially ordered sets,” Proceedings of the American Mathematical Society, vol. 7, no. 4, pp. 701–702, 1956.
- F. Galvin, “A proof of Dilworth's chain decomposition theorem,” American Mathematical Monthly, vol. 101, no. 4, pp. 352–353, 1994.
- M. A. Perles, “A proof of Dilworth's decomposition theorem for partially ordered sets,” Israel Journal of Mathematics, vol. 1, no. 2, pp. 105–107, 1963.
- H. Tverberg, “On Dilworth's decomposition theorem for partially ordered sets,” Journal of Combinatorial Theory, vol. 3, no. 3, pp. 305–306, 1967.
- R. H. Moehring, “Algorithmic aspects of comparability graphs and interval graphs,” in Graphs and Order, pp. 41–101, Reidel, Dordrecht, The Netherlands, 1985.
- A. A. Benczur, “Pushdown-reduce: an algorithm for connectivity augmentation and poset covering problems,” Discrete Applied Mathematics, vol. 129, no. 2-3, pp. 233–262, 2003.
- S. Felsner, V. Raghavan, and J. Spinrad, “Recognition algorithms for orders of small width and graphs of small Dilworth number,” Order, vol. 20, no. 4, pp. 351–364, 2003.
- S. Ikiz and K. Vijay Garg, “Online algorithms for Dilworth's chain partition,” Tech. Rep., Parallel and Distributed Systems Laboratory, Department of Electrical and Computer Engineering, University of Texas at Austin.
- G. V. Jourdan, J. X. Rampon, and C. Jard, “Computing on-line the lattice of maximal antichains of posets,” Rapport de Recherche 2271, Inria, Paris, France, 1994.
- H. A. M. Daniels and M. Velikova, “Derivation of monotone decision models from noisy data,” IEEE Transactions on Systems, Man, and Cybernetics Part A, vol. 36, no. 5, pp. 705–710, 2006.
- M. Rademaker, B. de Baets, and H. de Meyer, “Optimal monotone relabelling of partially non-monotone ordinal data,” Optimization Methods and Software, vol. 27, no. 1, pp. 17–31, 2012.
- E. Ciurea and L. Ciupalâ, “Sequential and parallel algorithms for minimum flows,” Journal of Applied Mathematics and Computing, vol. 15, no. 1-2, pp. 53–75, 2004.
- R. K. Ahuja, T. L. Magnanti, and J. B. Orlin, Network Flows: Theory, Algorithms, and Applications, Prentice Hall, New York, NY, USA, 1993.
- A. Schrijver, Combinatorial Optimization, Polyhedra and Efficiency, Springer, New York, NY, USA, 2003.