Abstract
We present a polynomial algorithm, implicit in the work of El-Zahar and Sauer, which inputs a 3-colouring of a categorical product of two graphs and outputs a 3-colouring of one of the factors. We raise a question about the existence of polynomial algorithms for colouring the vertices of some graphs in terms of intrinsic succint description of the vertices rather than in terms of the (exponential) size of the graph.
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References
M. El-Zahar, N. Sauer, The chromatic number of the product of two 4-chromatic graphs is 4, Combinatorica 5 (1985), 121–126.
S. H. Hedetniemi, Homomorphisms of graphs and automata, University of Michigan Technical Report 03105-44-T, 1966.
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© 2006 Springer-Verlag Berlin Heidelberg
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Tardif, C. (2006). On the Algorithmic Aspects of Hedetniemi’s Conjecture. In: Klazar, M., Kratochvíl, J., Loebl, M., Matoušek, J., Valtr, P., Thomas, R. (eds) Topics in Discrete Mathematics. Algorithms and Combinatorics, vol 26. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-33700-8_24
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DOI: https://doi.org/10.1007/3-540-33700-8_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-33698-3
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