Geodesic
Problems remaining NP-complete for sparse or dense graphs
Discussiones Mathematicae. Graph Theory, Tome 15 (1995) no. 1, pp. 33-41.

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For each fixed pair α,c > 0 let INDEPENDENT SET (m ≤ cn^α) and INDEPENDENT SET (m ≥ (ⁿ₂) - cn^α) be the problem INDEPENDENT SET restricted to graphs on n vertices with m ≤ cn^α or m ≥ (ⁿ₂) - cn^α edges, respectively. Analogously, HAMILTONIAN CIRCUIT (m ≤ n + cn^α) and HAMILTONIAN PATH (m ≤ n + cn^α) are the problems HAMILTONIAN CIRCUIT and HAMILTONIAN PATH restricted to graphs with m ≤ n + cn^α edges. For each ϵ > 0 let HAMILTONIAN CIRCUIT (m ≥ (1 - ϵ)(ⁿ₂)) and HAMILTONIAN PATH (m ≥ (1 - ϵ)(ⁿ₂)) be the problems HAMILTONIAN CIRCUIT and HAMILTONIAN PATH restricted to graphs with m ≥ (1 - ϵ)(ⁿ₂) edges.
Keywords: Computational Complexity, NP-Completeness, Hamiltonian Circuit, Hamiltonian Path, Independent Set 
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Schiermeyer, Ingo. Problems remaining NP-complete for sparse or dense graphs. Discussiones Mathematicae. Graph Theory, Tome 15 (1995) no. 1, pp. 33-41. http://geodesic.mathdoc.fr/item/DMGT_1995_15_1_a3/

[1] J. A. Bondy, Longest paths and cycles in graphs of high degree, Research Report CORR 80-16, Dept. of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada (1980).

[2] J. A. Bondy and U. S. R. Murty, Graph Theory with Applications (Macmillan, London and Elsevier, New York, 1976).

[3] H. J. Broersma, J. van den Heuvel and H. J. Veldman, A generalization of Ore's Theorem involving neighborhood unions, Discrete Math. 122 (1993) 37-49, doi: 10.1016/0012-365X(93)90285-2.

[4] G. A. Dirac, Some theorems on abstract graphs, Proc. London Math. Soc. 2 (1952) 69-81, doi: 10.1112/plms/s3-2.1.69.

[5] E. Flandrin, H. A. Jung and H. Li, Hamiltonism, degree sum and neighborhood intersections, Discrete Math. 90 (1991) 41-52, doi: 10.1016/0012-365X(91)90094-I.

[6] M. R. Garey and D. S. Johnson, Computers and I, A Guide to the Theory of NP-Completeness (Freeman, San Francisco, 1979).

[7] J. Kratochvíl, P. Savický and Z. Tuza, One more occurrence of variables makes jump from trivial to NP-complete, SIAM J. Comput. 22 (1993) 203-210, doi: 10.1137/0222015.

[8] O. Ore, Note on Hamiltonian circuits, Amer. Math. Monthly 67 (1960) 55, doi: 10.2307/2308928.

[9] I. Schiermeyer, The k-Satisfiability problem remains NP-complete for dense families, Discrete Math. 125 (1994) 343-346, doi: 10.1016/0012-365X(94)90175-9.