Problems remaining NP-complete for sparse or dense graphs

Schiermeyer, Ingo

Discussiones Mathematicae. Graph Theory, Tome 15 (1995) no. 1, pp. 33-41

Résumé

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.

Détail

Keywords: Computational Complexity, NP-Completeness, Hamiltonian Circuit, Hamiltonian Path, Independent Set