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Mathematical definitions of enclave and exclave, and applications

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  • Suzuki, Shinji
  • Inohara, Takehiro

Abstract

This paper offers mathematical definitions of enclave and exclave using a graph theoretical framework, and gives some applications of the definitions. Some basic properties of enclave and exclave are also verified by using the definitions. Though there are numerous enclaves and exclaves in the world, they have not been analyzed mathematically so far. Giving them mathematical definitions is useful for the problems of political boundaries, e.g. the drawing of the boundaries of single member electoral districts and the economic analysis of political integration.

Suggested Citation

  • Suzuki, Shinji & Inohara, Takehiro, 2015. "Mathematical definitions of enclave and exclave, and applications," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 728-742.
    • Handle: RePEc:eee:apmaco:v:268:y:2015:i:c:p:728-742
    DOI: 10.1016/j.amc.2015.06.114
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    1. Patrick Bolton & Gérard Roland, 1997. "The Breakup of Nations: A Political Economy Analysis," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(4), pages 1057-1090.
    2. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    3. Pradeep Dubey & Lloyd S. Shapley, 1979. "Mathematical Properties of the Banzhaf Power Index," Mathematics of Operations Research, INFORMS, vol. 4(2), pages 99-131, May.
    4. Shapley, L. S. & Shubik, Martin, 1954. "A Method for Evaluating the Distribution of Power in a Committee System," American Political Science Review, Cambridge University Press, vol. 48(3), pages 787-792, September.
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