- Tytuł:
- Problems remaining NP-complete for sparse or dense graphs
- Autorzy:
- Schiermeyer, Ingo
- Powiązania:
- https://bibliotekanauki.pl/articles/972006.pdf
- Data publikacji:
- 1995
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
Computational Complexity
NP-Completeness
Hamiltonian Circuit
Hamiltonian Path
Independent Set - Opis:
-
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.
We prove that these six restricted problems remain NP-complete. Finally, we consider sufficient conditions for a graph to have a Hamiltonian circuit. These conditions are based on degree sums and neighborhood unions of independent vertices, respectively. Lowering the required bounds the problem HAMILTONIAN CIRCUIT jumps from 'easy' to 'NP-complete'. - Źródło:
-
Discussiones Mathematicae Graph Theory; 1995, 15, 1; 33-41
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł