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Locally bounded k-colorings of trees

Published online by Cambridge University Press:  28 January 2009

C. Bentz  and
C. Picouleau
C. Bentz
Affiliation:
CEDRIC, CNAM, Paris, France; cedric.bentz@cnam.fr
C. Picouleau
Affiliation:
CEDRIC, CNAM, Paris, France; chp@cnam.fr
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Abstract

Given a tree T with n vertices, we show, by using a dynamicprogramming approach, that the problem of finding a 3-coloring ofT respecting local (i.e., associated with p prespecified subsetsof vertices) color bounds can be solved in O(n6p-1 logn)time. We also show that our algorithm can be adapted to the case ofk-colorings for fixed k.

Keywords

Bounded graph coloringtreedynamic programming.

Information

Type
Research Article
Information
RAIRO - Operations Research , Volume 43 , Issue 1 , January 2009 , pp. 27 - 33
Copyright
© EDP Sciences, ROADEF, SMAI, 2009

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References

Baker, B.S. and Coffman, E.G., Mutual exclusion scheduling. Theor. Comput. Sci. 162 (1996) 225–243. CrossRef
C. Berge, Graphes. Gauthier-Villars, Paris (1983).
Bodlaender, H.L. and Fomin, F.V., Equitable colorings of bounded treewidth graphs. Theor. Comput. Sci. 349 (2005) 22–30. CrossRef
Bodlaender, H.L. and Jansen, K., Restrictions of graph partition problems. Part I. Theor. Comput. Sci. 148 (1995) 93–109. CrossRef
B. Bollobás and R. Guy, Equitable and proportional coloring of trees. J. Comb. Theory, Ser. B 34 (1983) 177–186.
Chen, B.-L. and Lih, K.-W., A note on the m-bounded chromatic number of a tree. Eur. J. Comb. 14 (1993) 311–312. CrossRef
B.-L. Chen and K.-W. Lih, Equitable Coloring of Trees. J. Comb. Theory, Ser. B 61 (1994) 83–87.
T. Cormen, C. Leiserson, R. Rivest and C. Stein, Introduction to Algorithms. The MIT press, (2001).
de Werra, D., Hertz, A., Kobler, D. and Mahadev, N.V.R., Feasible edge colorings of trees with cardinality constraints. Discrete Math. 222 (2000) 61–72. CrossRef
M.R. Garey and D.S. Johnson, Computers and Intractability, a Guide to the Theory of NP-Completeness. Ed. Freeman New York (1979).
Gravier, S., Kobler, D. and Kubiak, W., Complexity of list coloring problems with a fixed total number of colors. Discrete Appl. Math. 117 (2002) 65–79. CrossRef
A. Hajnal and E. Szemerédi, Proof of a conjecture of P. Erdős. Combinatorial Theory and its Applications, Vol. II, North-Holland, Amsterdam (1970) 601–623.
Hansen, P., Hertz, A. and Kuplinsky, J., Bounded vertex colorings of graphs. Discrete Math. 111 (1993) 305–312. CrossRef
Jarvis, M. and Zhou, B., Bounded vertex coloring of trees. Discrete Math. 232 (2001) 145–151. CrossRef