Abstract
In contrast to the extremal variants of coNP-complete problems, which are frequently DP-complete, many extremal variants of NP-complete problems are in P. We investigate the extremal variants of two NP-complete problems, the extremal colorability problem with restricted degree and the extremal unfrozen non-implicant problem, and show that both of them are DP-complete.
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References
Abbas, N., Culberson, J., Stewart, L.: Recognizing maximal unfrozen graphs with respect to independent sets is coNP-complete. Discrete Mathematics & Theoretical Computer Science 7(1), 141–154 (2005)
Beacham, A., Culberson, J.: On the complexity of unfrozen problems. Discrete Applied Mathematics 153(1-3), 3–24 (2005)
Cai, J.-Y., Meyer, G.E.: Graph minimal uncolorability is DP-complete. SIAM Journal on Computing 16(2), 259–277 (1987)
Cai, J., Meyer, G.E.: On the complexity of graph critical uncolorability. In: Ottmann, T. (ed.) ICALP 1987. LNCS, vol. 267, pp. 394–403. Springer, Heidelberg (1987)
Cheng, Y., Ko, K.-I., Wu, W.: On the complexity of non-unique probe selection. Theoretical Computer Science 390(1), 120–125 (2008)
Chvátal, V., Szemerédi, E.: Many hard examples for resolution. Journal of the ACM 35, 759–768 (1988)
Emden-Weinert, T., Hougardy, S., Kreuter, B.: Uniquely colourable graphs and the hardness of colouring graphs of large girth. Combinatorics, Probability and Computing 7(4), 375–386 (1998)
Garey, M.R., Johnson, D.S., Stockmeyer, L.: Some simplified NP-complete graph problems. Theoretical Computer Science 1(3), 237–267 (1976)
Goldsmith, J., Hagen, M., Mundhenk, M.: Complexity of DNF and isomorphism of monotone formulas. In: Jedrzejowicz, J., Szepietowski, A. (eds.) MFCS 2005. LNCS, vol. 3618, pp. 410–421. Springer, Heidelberg (2005)
Kolaitis, P.G., Martin, D.L., Thakur, M.N.: On the complexity of the containment problem for conjunctive queries with built-in predicates. In: PODS 1998: Proceedings of the 17th ACM SIGACT-SIGMOD-SIGART symposium on Principles of Database Systems, pp. 197–204. ACM, New York (1998)
Papadimitriou, C.H.: Computational Complexity. Addison-Wesley, Reading (1994)
Papadimitriou, C.H., Yannakakis, M.: The complexity of facets (and some facets of complexity). In: STOC 1982: Proceedings of the 14th annual ACM symposium on Theory of Computing, pp. 255–260. ACM, New York (1982)
Papadimitriou, C.H., Wolfe, D.: The complexity of facets resolved. Journal of Computer and System Sciences 37(1), 2–13 (1988)
Riege, T., Rothe, J.: Completeness in the boolean hierarchy: Exact-four-colorability, minimal graph uncolorability, and exact domatic number problems - a survey. Journal of Universal Computer Science 12(5), 551–578 (2006)
Rothe, J.: Exact complexity of exact-four-colorability. Information Processing Letters 87(1), 7–12 (2003)
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Cao, Y., Culberson, J., Stewart, L. (2009). DP-Complete Problems Derived from Extremal NP-Complete Properties. In: Královič, R., Niwiński, D. (eds) Mathematical Foundations of Computer Science 2009. MFCS 2009. Lecture Notes in Computer Science, vol 5734. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03816-7_18
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DOI: https://doi.org/10.1007/978-3-642-03816-7_18
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