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w-Density and w-balanced property of weighted graphs

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Abstract

The notion of w-density for the graphs with positive weights on vertices and nonnegative weights on edges is introduced. A weighted graph is called w-balanced if its w-density is no less than the w-density of any subgraph of it. In this paper, a good characterization of w-balanced weighted graphs is given. Applying this characterization, many large w-balanced weighted graphs are formed by combining smaller ones. In the case where a graph is not w-balanced, a polynomial-time algorithm to find a subgraph of maximum w-density is proposed. It is shown that the w-density theory is closely related to the study of SEW (G,w) games.

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References

  1. Bondy, J. A., Murty, U. S. R., Graph Theory with Applications, Macmillan, London and Elsevier, New York, 1976.

    Google Scholar 

  2. Deng, X., Mathematical programming: Complexity and algorithms, Ph. D. Thesis, Department of Operations Research, Stanford University, California, 1989.

    Google Scholar 

  3. Deng, X., Combinatorial optimization and coalition games, In: Du and Pardalos eds., Handbook of Combinatorial Optimization, Kluwer Academic Publishers, 1998, 1–27.

  4. Deng, X., Papadimitriou, C. H., On the complexity of cooperative solution concepts, Mathematics of Operations Research, 1994, 19(2):257–266.

    Article  MATH  MathSciNet  Google Scholar 

  5. Erdös, P., Rényi, A., On the evolution of random graphs, Publ. Math. Inst. Hung. Acad. Sci., 1960, 5: 17–61.

    MATH  Google Scholar 

  6. Karoński, M., A review of random graphs, J. Graph Theory, 1982, 6: 349–389.

    Article  MATH  MathSciNet  Google Scholar 

  7. Penrice, S.G., Balanced graphs and network flows, Networks, 1997, 29: 77–80.

    Article  MATH  MathSciNet  Google Scholar 

  8. Picard, J. C., Queyanne, M., A network flow solution to some nonlinear 0–1 programming problems, with applications to graph theory, Networks, 1982, 12: 141–159.

    Article  MATH  MathSciNet  Google Scholar 

  9. Picard, J. C., Ratliff, H. D., Minimum cuts and related problems, Networks, 1974, 5: 357–370.

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Dept. of Appl. Math., Northwestern Polytechnical Univ., 710072, Xi’an, China

    Zhang Shenggui & Sun Hao

  2. Center of Combinatorics, Nankai Univ., 300071, Tianjin, China

    Li Xueliang

Authors
  1. Zhang Shenggui
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  2. Sun Hao
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  3. Li Xueliang
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Supported by the National Natural Science Foundation of China (10101021).

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Shenggui, Z., Hao, S. & Xueliang, L. w-Density and w-balanced property of weighted graphs. Appl. Math. Chin. Univ. 17, 355–364 (2002). https://doi.org/10.1007/s11766-002-0015-9

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  • DOI: https://doi.org/10.1007/s11766-002-0015-9

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