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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 93, Issue 1
  • January 1983, pp. 9-23

Determining the thickness of graphs is NP-hard

  • Anthony Mansfield (a1)
  • DOI: http://dx.doi.org/10.1017/S030500410006028X
  • Published online: 24 October 2008
Abstract
Abstract

The thickness of a graph is a measure of its nonplanarity and has applications in the theory of printed circuits. To determine the thickness of an arbitrary graph is a seemingly intractable problem. This is made precise in this paper where we answer an open problem of Garey and Johnson (2) by proving that it is NP-complete to decide whether a graph has thickness two.

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(3)I. Holyer The NP-completeness of edge colouring. SIAM J. Comput. 10 (1981), 718720.

(4)J. E. Hopcroft and R. E. Tarjan Efficient planarity testing. J. Ass. Comput. Mach. 21 (1974), 549568.

(5)D. Lichtenstein Planar formulae and their uses. SIAM J. Comput. 11 (1982), 329343.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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