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Interchangeability of Relevant Cycles in Graphs

Author

Listed:
  • Petra M. Gleiss
  • Josef Leydold
  • Peter F. Stadler

Abstract

The set R of relevant cycles of a graph G is the union of its minimum cycle bases. We introduce a partition of R such that each cycle in a class W can be expressed as a sum of other cycles and W and shorter cycles. It is shown that each minimum cycle basis contains the same number of representatives of a given class W. This result is used to derive upper and lower bounds on the number of distinct minimum cycle bases. Finally, we give a polynomial-time algorithm to compute this partition.

Suggested Citation

  • Petra M. Gleiss & Josef Leydold & Peter F. Stadler, 1999. "Interchangeability of Relevant Cycles in Graphs," Working Papers 99-07-046, Santa Fe Institute.
  • Handle: RePEc:wop:safiwp:99-07-046
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    References listed on IDEAS

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    1. Neyman, Abraham, 1985. "Bounded complexity justifies cooperation in the finitely repeated prisoners' dilemma," Economics Letters, Elsevier, vol. 19(3), pages 227-229.
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    3. Abreu, Dilip & Rubinstein, Ariel, 1988. "The Structure of Nash Equilibrium in Repeated Games with Finite Automata," Econometrica, Econometric Society, vol. 56(6), pages 1259-1281, November.
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    5. Bacharach, M. & Shin, H.S. & Williams, M., 1992. "Sophisticated Bounded Agents Play the Repeated Dilemma," Economics Series Working Papers 99143, University of Oxford, Department of Economics.
    6. Radner, Roy, 1980. "Collusive behavior in noncooperative epsilon-equilibria of oligopolies with long but finite lives," Journal of Economic Theory, Elsevier, vol. 22(2), pages 136-154, April.
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    Keywords

    Minimum cycle basis; relevant cycles;

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