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Problems remaining NP-complete for sparse or dense graphs

Ingo Schiermeyer (1995)

Discussiones Mathematicae Graph Theory

For each fixed pair α,c > 0 let INDEPENDENT SET ( m c n α ) and INDEPENDENT SET ( m ( ) - c n α ) be the problem INDEPENDENT SET restricted to graphs on n vertices with m c n α or m ( ) - c n α edges, respectively. Analogously, HAMILTONIAN CIRCUIT ( m n + c n α ) and HAMILTONIAN PATH ( m n + c n α ) are the problems HAMILTONIAN CIRCUIT and HAMILTONIAN PATH restricted to graphs with m n + c n 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...

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