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Uniqueness of colorability and colorability of planar 4-regular graphs are NP-complete

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David P. DaileyAuthors Info & Claims

Discrete Mathematics, Volume 30, Issue 3

Pages 289 - 293

https://doi.org/10.1016/0012-365X(80)90236-8

Published: 01 January 1980 Publication History

Abstract

It is shown that two sorts of problems belong to the NP-complete class. First, it is proven that for a given @k-colorable graph and a given @k-coloring of that graph, determining whether the graph is or is not uniquely @k-colorable is NP-complete. Second, a result by Garey, Johnson, and Stockmeyer is extended with a proof that the coloring of four-regular planar graphs is NP-complete.

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Dailey, D.P., Graph coloring by humans and machines. In: Ph.D. Thesis, University of Colorado, Boulder, CO.

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Cook, S.A., The complexity of theorem-proving procedures. In: Proceedings, Third Annual ACM Computing Theory Symposium,

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Karp, R.M., Reducibility among combinatorial problems. In: Miller, R.E., Thatcher, J.W. (Eds.), Complexity of Computer Computations, Plenum Press, New York.

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Garey, M.R., Johnson, D.S. and Stockmeyer, L., Some simplified NP-complete graph problems. Theoretical Computer Science. v1. 237-267.

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Aho, A.V., Hopcroft, J.E. and Ullman, J.D., The design and Analysis of Computer Algorithms. 1974. Addison-Wesley, Reading, MA.

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Garey, M.R. and Johnson, D.S., Computers and Intractability: A Guide to the Theory of NP-Completeness. 1979. Freeman, San Francisco.

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Stockmeyer, L., Planar 3-colorability is polynomial complete. SIGACT News. 19-25.

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Uniqueness of colorability and colorability of planar 4-regular graphs are NP-complete
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Graph algorithms
      2. Graph enumeration

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Discrete Mathematics Volume 30, Issue 3

January, 1980

113 pages

ISSN:0012-365X

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Elsevier Science Publishers B. V.

Netherlands

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Published: 01 January 1980

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The (3,3)-colorability of planar graphs without 4-cycles and 5-cycles

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On the 7 Total Colorability of Planar Graphs with Maximum Degree 6 and without 4-cycles

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