Abstract
In this paper we describe and analyze an improved algorithm for deciding the 3-Colourability problem. If G is a simple graph on n vertices then we will show that this algorithm tests a graph for 3-Colourability, i.e. an assignment of three colours to the vertices of G such that two adjacent vertices obtain different colours, in less than O(1.415n) steps.
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References
J. A. Bondy and U. S. R. Murty, Graph Theory with Applications (Macmillan, London and Elsevier, New York, 1976).
N. Christofides, An Algorithm for the Chromatic Number of a Graph, Computer J. 14(1971)38–39.
M. R. Garey and D. S. Johnson, Computers and Intractability, A Guide to the Theory of N P-Completeness, W. H. Freeman and Company, New York, 1979.
M. R. Garey and D. S. Johnson, The complexity of Near-Optimal Graph Coloring, J. ACM 23 (1976) 43–49.
D. S. Johnson, The NP-Completeness Column: An Ongoing Guide, J. of Alg. 13 (1992) 502–524.
E. L. Lawler, A Note on the Complexity of the Chromatic Number Problem, Inform. Process. Lett. 5 (1976) 66–67.
J. W. Moon and L. Moser, On Cliques in Graphs, Israel J. of Math. 3 (1965) 23–28.
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© 1994 Springer-Verlag Berlin Heidelberg
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Schiermeyer, I. (1994). Deciding 3-colourability in less than O(1.415n) steps. In: van Leeuwen, J. (eds) Graph-Theoretic Concepts in Computer Science. WG 1993. Lecture Notes in Computer Science, vol 790. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57899-4_51
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DOI: https://doi.org/10.1007/3-540-57899-4_51
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-57899-4
Online ISBN: 978-3-540-48385-4
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