Elsevier

Theoretical Computer Science

Volume 1, Issue 3, February 1976, Pages 237-267
Theoretical Computer Science

Some simplified NP-complete graph problems

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Abstract

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.

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The work of this author was done, in part, at Project MAC, and supported by the National Science Foundation under research grant GJ-34671; present address: IBM Thomas J. Watson Research Center, Yorktown Heights, N.Y.