Abstract
In their paper, C.H.Papadimitriou and M.Yannakakis [PY] posed the problem of classifying the complexity of graph critical uncolorability; and in particular, they asked whether the minimal-3-uncolorability problem is DP-complete. This paper gives an affirmative answer to the above question. We show that minimal-k-uncolorability is DP-complete, for all fixed k≥3. Furthermore, the reduction can be modified by using “sensitive” transformations to resolve the planar case (for k=3), bounded vertex degree case and their combination.
Research supported by NSF grant DCR-8301766.
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© 1987 Springer-Verlag Berlin Heidelberg
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Cai, Jy., Meyer, G.E. (1987). On the complexity of graph critical uncolorability. In: Ottmann, T. (eds) Automata, Languages and Programming. ICALP 1987. Lecture Notes in Computer Science, vol 267. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-18088-5_34
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DOI: https://doi.org/10.1007/3-540-18088-5_34
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