1974/01/01 by M. R. Garey, D. S. Johnson, Larry Stockmeyer · 12 citations
Computer Science · Mathematics · #Advanced Graph Theory Research #Algorithm #Combinatorics #Complexity and Algorithms in Graphs #Computational Geometry and Mesh Generation #Computational complexity theory #Corollary #Discrete mathematics #Graph #Hamiltonian path #Hamiltonian path problem #Mathematics #Maximum cut #NP-complete #Time complexity #Undirected graph #Upper and lower bounds
paper · pdf · doi:10.1145/800119.803884
openalex publication_date 1974/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08
It is widely believed that showing a problem to be NP-complete is tantamount to proving its computational intractability. In this paper we show that a number of NP-complete problems remain NP-complete even when their domains are substantially restricted. First we show the completeness of SIMPLE MAX CUT (MAX CUT with edge weights restricted to value 1), and, as a corollary, the completeness of the OPTIMAL LINEAR ARRANGEMENT problem. We then show that even if the domains of the NODE COVER and DIRECTED HAMILTONIAN PATH problems are restricted to planar graphs, the two problems remain NP-complete, and that these and other graph problems remain NP-complete even when their domains are restricted to graphs with low node degrees. For GRAPH 3-COLORABILITY, NODE COVER, and UNDIRECTED HAMILTONIAN CIRCUIT, we determine essentially the lowest possible upper bounds on node degree for which the problems remain NP-complete.