Abstract
We discuss the Precoloring Extension (PrExt) and the List Coloring (LiCol) problems for trees, partial k-trees and cographs in the decision and the construction versions. Both problems for partial k-trees are solved in linear time, when the number of colors is a constant and by O(¦V¦k+2)-algorithmsin general. For trees, we improve this to linear time. In contrast to that, PrExt and LiCol differ in complexity for cographs. While the first has a linear algorithm, the second is shown NP-complete. We give polynomial algorithms for the corresponding enumeration problems #PrExt and #LiCol on partial k-trees and trees and for #PrExt on cographs.
Supported in part by Deutsche Forschungsgemeinschaft
Supported by KAI e. V. under contract 014300/I
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© 1993 Springer-Verlag Berlin Heidelberg
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Jansen, K., Scheffler, P. (1993). Generalized coloring for tree-like graphs. In: Mayr, E.W. (eds) Graph-Theoretic Concepts in Computer Science. WG 1992. Lecture Notes in Computer Science, vol 657. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56402-0_35
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DOI: https://doi.org/10.1007/3-540-56402-0_35
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