Polynomial algorithms that prove an NP-Hard hypothesis implies an NP-hard conclusion

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Bauer, D. and Broersma, H.J. and Morgana, A. and Schmeichel, E. (2002) Polynomial algorithms that prove an NP-Hard hypothesis implies an NP-hard conclusion. Discrete Applied Mathematics, 120 (1-3). pp. 13-23. ISSN 0166-218X

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Abstract:An example of such a theorem is the well-known Chvátal–Erdős Theorem, which states that every graph G with ακ is hamiltonian. Here κ is the vertex connectivity of G and α is the cardinality of a largest set of independent vertices of G. In another paper Chvátal points out that the proof of this result is in fact a polynomial time construction that either produces a Hamilton cycle or a set of more than κ independent vertices. In this note we point out that other theorems in hamiltonian graph theory have a similar character. In particular, we present a constructive proof of a well-known theorem of Jung (Ann. Discrete Math. 3 (1978) 129) for graphs on 16 or more vertices.
Item Type:Article
Copyright:© 2002 Elsevier
Faculty:
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/74833
Official URL:http://dx.doi.org/10.1016/S0166-218X(01)00276-1
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