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Determining the thickness of graphs is NP-hard

  • Anthony Mansfield (a1)

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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(1)Beineke, L. W. and Wilson, R. J.Selected topics in graph theory (Academic Press, London, 1978).
(2)Garey, M. R. and Johnson, D. S.Computers and intractability a guide to the theory of NP-completeness (Freeman, San Francisco, 1979).
(3)Holyer, I.The NP-completeness of edge colouring. SIAM J. Comput. 10 (1981), 718720.
(4)Hopcroft, J. E. and Tarjan, R. E.Efficient planarity testing. J. Ass. Comput. Mach. 21 (1974), 549568.
(5)Lichtenstein, D.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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