Locally bounded k-colorings of trees
RAIRO - Operations Research - Recherche Opérationnelle, Tome 43 (2009) no. 1, pp. 27-33.

Given a tree T with n vertices, we show, by using a dynamic programming approach, that the problem of finding a 3-coloring of T respecting local (i.e., associated with p prespecified subsets of vertices) color bounds can be solved in O(n 6p-1 logn) time. We also show that our algorithm can be adapted to the case of k-colorings for fixed k.

DOI : 10.1051/ro/2009003
Classification : 05C15, 90C39
Mots clés : bounded graph coloring, tree, dynamic programming
@article{RO_2009__43_1_27_0,
     author = {Bentz, C. and Picouleau, C.},
     title = {Locally bounded $k$-colorings of trees},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {27--33},
     publisher = {EDP-Sciences},
     volume = {43},
     number = {1},
     year = {2009},
     doi = {10.1051/ro/2009003},
     mrnumber = {2502323},
     zbl = {1158.05317},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ro/2009003/}
}
TY  - JOUR
AU  - Bentz, C.
AU  - Picouleau, C.
TI  - Locally bounded $k$-colorings of trees
JO  - RAIRO - Operations Research - Recherche Opérationnelle
PY  - 2009
SP  - 27
EP  - 33
VL  - 43
IS  - 1
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/ro/2009003/
DO  - 10.1051/ro/2009003
LA  - en
ID  - RO_2009__43_1_27_0
ER  - 
%0 Journal Article
%A Bentz, C.
%A Picouleau, C.
%T Locally bounded $k$-colorings of trees
%J RAIRO - Operations Research - Recherche Opérationnelle
%D 2009
%P 27-33
%V 43
%N 1
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/ro/2009003/
%R 10.1051/ro/2009003
%G en
%F RO_2009__43_1_27_0
Bentz, C.; Picouleau, C. Locally bounded $k$-colorings of trees. RAIRO - Operations Research - Recherche Opérationnelle, Tome 43 (2009) no. 1, pp. 27-33. doi : 10.1051/ro/2009003. http://www.numdam.org/articles/10.1051/ro/2009003/

[1] B.S. Baker and E.G. Coffman, Mutual exclusion scheduling. Theor. Comput. Sci. 162 (1996) 225-243. | MR | Zbl

[2] C. Berge, Graphes. Gauthier-Villars, Paris (1983). | MR | Zbl

[3] H.L. Bodlaender and F.V. Fomin, Equitable colorings of bounded treewidth graphs. Theor. Comput. Sci. 349 (2005) 22-30. | MR | Zbl

[4] H.L. Bodlaender and K. Jansen, Restrictions of graph partition problems. Part I. Theor. Comput. Sci. 148 (1995) 93-109. | MR | Zbl

[5] B. Bollobás and R. Guy, Equitable and proportional coloring of trees. J. Comb. Theory, Ser. B 34 (1983) 177-186. | MR | Zbl

[6] B.-L. Chen and K.-W. Lih, A note on the m-bounded chromatic number of a tree. Eur. J. Comb. 14 (1993) 311-312. | MR | Zbl

[7] B.-L. Chen and K.-W. Lih, Equitable Coloring of Trees. J. Comb. Theory, Ser. B 61 (1994) 83-87. | MR | Zbl

[8] T. Cormen, C. Leiserson, R. Rivest and C. Stein, Introduction to Algorithms. The MIT press, (2001). | MR | Zbl

[9] D. De Werra, A. Hertz, D. Kobler and N.V.R. Mahadev, Feasible edge colorings of trees with cardinality constraints. Discrete Math. 222 (2000) 61-72. | MR | Zbl

[10] M.R. Garey and D.S. Johnson, Computers and Intractability, a Guide to the Theory of NP-Completeness. Ed. Freeman New York (1979). | MR | Zbl

[11] S. Gravier, D. Kobler and W. Kubiak, Complexity of list coloring problems with a fixed total number of colors. Discrete Appl. Math. 117 (2002) 65-79. | MR | Zbl

[12] 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. | MR | Zbl

[13] P. Hansen, A. Hertz and J. Kuplinsky, Bounded vertex colorings of graphs. Discrete Math. 111 (1993) 305-312. | MR | Zbl

[14] M. Jarvis and B. Zhou, Bounded vertex coloring of trees. Discrete Math. 232 (2001) 145-151. | MR | Zbl

Cité par Sources :