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Coloring fuzzy graphs

Author

Listed:
  • Muñoz, Susana
  • Teresa Ortuño, M.
  • Ramírez, Javier
  • Yáñez, Javier

Abstract

Given a graph G=(V,E), a coloring function C assigns an integer value C(i) to each node i[set membership, variant]V in such a way that the extremes of any edge {i,j}[set membership, variant]E cannot share the same color, i.e., C(i)[not equal to]C(j). Two different approaches to the graph coloring problem of a fuzzy graph are introduced in this paper. The classical concept of the (crisp) chromatic number of a graph is generalized for these approaches. The first approach is based on the successive coloring functions C[alpha] of the crisp graphs G[alpha]=(V,E[alpha]), the [alpha]-cuts of ; the traffic lights problem is analyzed following this approach. The second approach is based on an extension of the concept of coloring function by means of a distance defined between colors; a timetabling problem is analyzed within this approach. An exact algorithm for obtaining the chromatic number associated with the second approach is proposed, and some computational results on randomly generated fuzzy graphs are reported.

Suggested Citation

  • Muñoz, Susana & Teresa Ortuño, M. & Ramírez, Javier & Yáñez, Javier, 2005. "Coloring fuzzy graphs," Omega, Elsevier, vol. 33(3), pages 211-221, June.
    • Handle: RePEc:eee:jomega:v:33:y:2005:i:3:p:211-221
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    References listed on IDEAS

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    1. Anuj Mehrotra & Michael A. Trick, 1996. "A Column Generation Approach for Graph Coloring," INFORMS Journal on Computing, INFORMS, vol. 8(4), pages 344-354, November.
    2. Samuel Eilon & Nicos Christofides, 1971. "The Loading Problem," Management Science, INFORMS, vol. 17(5), pages 259-268, January.
    3. Avanthay, Cedric & Hertz, Alain & Zufferey, Nicolas, 2003. "A variable neighborhood search for graph coloring," European Journal of Operational Research, Elsevier, vol. 151(2), pages 379-388, December.
    4. J. Randall Brown, 1972. "Chromatic Scheduling and the Chromatic Number Problem," Management Science, INFORMS, vol. 19(4-Part-1), pages 456-463, December.
    5. Thomas J. Sager & Shi-Jen Lin, 1991. "A Pruning Procedure for Exact Graph Coloring," INFORMS Journal on Computing, INFORMS, vol. 3(3), pages 226-230, August.
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    Cited by:

    1. Isnaini Rosyida & Jin Peng & Lin Chen & Widodo Widodo & Ch. Rini Indrati & Kiki A. Sugeng, 2018. "An uncertain chromatic number of an uncertain graph based on $$\alpha $$ α -cut coloring," Fuzzy Optimization and Decision Making, Springer, vol. 17(1), pages 103-123, March.
    2. Sovan Samanta & Madhumangal Pal, 2013. "Fuzzy k-competition graphs and p-competition fuzzy graphs," Fuzzy Information and Engineering, Springer, vol. 5(2), pages 191-204, June.

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