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Random coloring evolution on graphs

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Abstract

In this short note we study how two colors, red and blue, painted on a given graph are evolved randomly according to a transition rule which aims to simulate how people influence each other. We shall also calculate the probability that the evolution will be trapped eventually using the martingale method.

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References

  1. Pittel, B.: On spreading a rumor. J. Appl. Math., 47(1), 213–223 (1987)

    MATH  MathSciNet  Google Scholar 

  2. Zhang, X., Liu, G. Z.: f-Colorings of some graphs of f-Class 1. Acta Mathematica Sinica, English Series, 24(5), 743–748 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  3. Matzinger, H., Rolles, S. W. W.: Finding blocks and other patterns in a random coloring of Z. Random Structures Algorithms, 28(1), 37–75 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  4. Fontes, L., Newman, C. M.: First passage percolation for random colorings of Z d. Ann. Appl. Probab., 3(3), 746–762 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  5. Chung, K. L.: Markov Chains with Stationary Transition Probabilities, 2nd ed., Springer-Verlag, Berlin, 1967

    MATH  Google Scholar 

  6. Feller, W.: An Introduction to Probability Theory and its Applications, Vol. I, John Wiley & Sons, 3rd edition, 1968

  7. Doob, J. L.: Stochastic Processes, Wiley, New York, 1953

    MATH  Google Scholar 

  8. Bollobas, B.: Modern Graph Theory, Springer-Verlag, New York, 1998

    MATH  Google Scholar 

  9. Kemeny, J. G., Snell, J. L.: Finite Markov Chains, Springer-Verlag, New York, 1960

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Shanghai Jiaotong University, Shanghai, 200240, P. R. China

    Xin Xing Chen

  2. Institute of Mathematics, Fudan University, Shanghai, 200433, P. R. China

    Jian Gang Ying

Authors
  1. Xin Xing Chen
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  2. Jian Gang Ying
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Corresponding author

Correspondence to Xin Xing Chen.

Additional information

The second author is supported by NSFC (Grant No. 10671036)

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Chen, X.X., Ying, J.G. Random coloring evolution on graphs. Acta. Math. Sin.-English Ser. 26, 369–376 (2010). https://doi.org/10.1007/s10114-010-6286-9

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  • DOI: https://doi.org/10.1007/s10114-010-6286-9

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