# Coloration de graphes : fondements et applications

Dominique de Werra; Daniel Kobler

RAIRO - Operations Research (2010)

- Volume: 37, Issue: 1, page 29-66
- ISSN: 0399-0559

## Access Full Article

top## Abstract

top## How to cite

topde Werra, Dominique, and Kobler, Daniel. "Coloration de graphes : fondements et applications." RAIRO - Operations Research 37.1 (2010): 29-66. <http://eudml.org/doc/105281>.

@article{deWerra2010,

abstract = {
The classical colouring models are well known thanks in large part to
their applications to scheduling type problems; we describe the basic
concepts of colourings together with a number of variations and
generalisations arising from scheduling problems such as the creation
of school schedules. Some exact and heuristic algorithms will be
presented, and we will sketch solution methods based on tabu search to
find approximate solutions to large problems. Finally we will also
mention the use of colourings for creating schedules in sports leagues
and for computer file transfer problems. This paper is an extended
version of [37].
},

author = {de Werra, Dominique, Kobler, Daniel},

journal = {RAIRO - Operations Research},

keywords = {colouring models; scheduling},

language = {eng},

month = {3},

number = {1},

pages = {29-66},

publisher = {EDP Sciences},

title = {Coloration de graphes : fondements et applications},

url = {http://eudml.org/doc/105281},

volume = {37},

year = {2010},

}

TY - JOUR

AU - de Werra, Dominique

AU - Kobler, Daniel

TI - Coloration de graphes : fondements et applications

JO - RAIRO - Operations Research

DA - 2010/3//

PB - EDP Sciences

VL - 37

IS - 1

SP - 29

EP - 66

AB -
The classical colouring models are well known thanks in large part to
their applications to scheduling type problems; we describe the basic
concepts of colourings together with a number of variations and
generalisations arising from scheduling problems such as the creation
of school schedules. Some exact and heuristic algorithms will be
presented, and we will sketch solution methods based on tabu search to
find approximate solutions to large problems. Finally we will also
mention the use of colourings for creating schedules in sports leagues
and for computer file transfer problems. This paper is an extended
version of [37].

LA - eng

KW - colouring models; scheduling

UR - http://eudml.org/doc/105281

ER -

## References

top- N. Alon et M. Tarsi, Colorings and orientations of graphs. Combinatorica12 (1992) 125-134.
- M. Bellare, O. Goldreich et M. Sudan, Free bits, PCPs and non-approximability - towards tight results. SIAM J. Comput.27 (1998) 804-915.
- C. Berge, Graphes. Gauthier-Villars, Paris (1983).
- C. Berge, Hypergraphes. Gauthier-Villars, Paris (1987).
- C. Berge et V. Chvátal, Topics on Perfect Graphs. Ann. Discrete Math. 21 (1984).
- M. Biró, M. Hujter et Zs. Tuza, Precoloring extension. I. Interval graphs. Discrete Math.100 (1992) 267-279.
- H.L. Bodlaender, K. Jansen et G. Woeginger, Scheduling with incompatible jobs. Discrete Appl. Math.55 (1994) 219-232.
- V. Chvátal, Perfectly ordered graphs, in Topics on Perfect Graphs. North Holland Math. Stud. 88, Annals Discrete Math. 21 (1984) 63-65.
- E.G. Coffman Jr., M.G. Garey, D.S. Johnson et A.S. Lapaugh, Scheduling file transfers. SIAM J. Comput.14 (1985) 744-780.
- O. Coudert, Exact Coloring of Real-Life Graphs is Easy, in Proc. of 34th ACM/IEEE Design Automation Conf. ACM Press, New York (1997) 121-126.
- N. Dubois et D. de Werra, EPCOT: An Efficient Procedure for Coloring Optimally with Tabu Search. Comput. Math. Appl.25 (1993) 35-45.
- K. Easton, G. Nemhauser et M. Trick, The traveling tournament problem: description and benchmarks. GSIA, Carnegie Mellon University (2002).
- C. Fleurent et J.A. Ferland, Genetic and Hybrid Algorithms for Graph Coloring, édité par G. Laporte et I.H. Osman (éds). Metaheuristics in Combinatorial Optimization, Ann. Oper. Res. 63 (1996) 437-461.
- M.G. Garey et D.S. Johnson, The complexity of near-optimal graph coloring. J. ACM23 (1976) 43-49.
- M.G. Garey, D.S. Johnson et L. Stockmeyer, Some simplified NP-complete graph problems. Theoret. Comput. Sci.1 (1976) 237-267.
- F. Glover et M. Laguna, Tabu Search. Kluwer Academic Publ. (1997).
- M.C. Golumbic, Algorithmic Graph Theory and Perfect Graphs. Academic Press, New York (1984).
- M. Grötschel, L. Lovasz et A. Schrijver, Geometric Algorithms and Combinatorial Optimization. Springer-Verlag, Berlin (1988).
- M.M. Halldórsson, A still better performance guarantee for approximate graph coloring. Inform. Process. Lett.45 (1993) 19-23.
- P. Hansen, A. Hertz et J. Kuplinsky, Bounded Vertex Colorings of Graphs. Discrete Math.111 (1993) 305-312.
- P. Hansen, J. Kuplinsky et D. de Werra, Mixed Graph Coloring. Math. Meth. Oper. Res.45 (1997) 145-160.
- A.J.W. Hilton et D. de Werra, A sufficient condition for equitable edge-colourings of simple graphs. Discrete Math.128 (1994) 179-201.
- E.L. Lawler, Combinatorial Optimization: Networks and Matroids. Holt, Rinehart and Winston, New York (1976).
- F. Leighton, A Graph Coloring Algorithm for Large Scheduling Problems. J. Res. National Bureau Standards84 (1979) 742-774.
- M. Middendorf et F. Pfeiffer, On the complexity of recognizing perfectly orderable graphs, Discrete Mathematics 80 (1990) 327-333.
- A. Pnueli, A. Lempel et S. Even, Transitive orientation of graphs and identification of permutation graphs. Canadian J. Math.23 (1971) 160-175.
- F.S. Roberts, Discrete Mathematical Models. Prentice-Hall, Englewood Cliffs (1976).
- Zs. Tuza, Graph colorings with local constraints - a survey, Discussiones Mathematicae - Graph Theory 17 (1997) 161-228.
- V.G. Vizing, On an estimate of the chromatic class of a p-graph (en russe), Metody Discret Analiz. 3 (1964) 25-30.
- D.J.A. Welsh et M.B. Powell, An upper bound on the chromatic number of a graph and its application to timetabling problems, Computer J. 10 (1967) 85-87.
- D. de Werra, Some models of graphs for scheduling sports competitions, Discrete Applied Mathematics 21 (1988) 47-65.
- D. de Werra, The combinatorics of timetabling, European Journal of Operational Research 96 (1997) 504-513.
- D. de Werra, On a multiconstrained model for chromatic scheduling, Discrete Applied Mathematics 94 (1999) 171-180.
- D. de Werra, Ch. Eisenbeis, S. Lelait et B. Marmol, On a graph-theoretical model for cyclic register allocation, Discrete Applied Mathematics 93 (1999) 191-203.
- D. de Werra et Y. Gay, Chromatic scheduling and frequency assignment, Discrete Applied Mathematics 49 (1994) 165-174.
- D. de Werra et A. Hertz, Consecutive colorings of graphs, Zeischrift für Operations Research 32 (1988) 1-8.
- D. de Werra et D. Kobler, Coloration et ordonnencement chromatique, ORWP 00/04, Ecole Polytechnique Fédérale de Lausanne, 2000.
- X. Zhou et T. Nishizeki, Graph Coloring Algorithms, IEICE Trans. on Information and Systems E83-D (2000) 407-417.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.