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
@article{DMGT_1995_15_1_a3,
author = {Schiermeyer, Ingo},
title = {Problems remaining {NP-complete} for sparse or dense graphs},
journal = {Discussiones Mathematicae. Graph Theory},
pages = {33--41},
publisher = {mathdoc},
volume = {15},
number = {1},
year = {1995},
language = {en},
url = {http://geodesic.mathdoc.fr/item/DMGT_1995_15_1_a3/}
}
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/