A Note on the Uniqueness of Stable Marriage Matching

Ewa Drgas-Burchardt

Discussiones Mathematicae Graph Theory (2013)

  • Volume: 33, Issue: 1, page 49-55
  • ISSN: 2083-5892

Abstract

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In this note we present some sufficient conditions for the uniqueness of a stable matching in the Gale-Shapley marriage classical model of even size. We also state the result on the existence of exactly two stable matchings in the marriage problem of odd size with the same conditions.

How to cite

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Ewa Drgas-Burchardt. "A Note on the Uniqueness of Stable Marriage Matching." Discussiones Mathematicae Graph Theory 33.1 (2013): 49-55. <http://eudml.org/doc/267608>.

@article{EwaDrgas2013,
abstract = {In this note we present some sufficient conditions for the uniqueness of a stable matching in the Gale-Shapley marriage classical model of even size. We also state the result on the existence of exactly two stable matchings in the marriage problem of odd size with the same conditions.},
author = {Ewa Drgas-Burchardt},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {stable matching; Gale-Shapley model; stable perfect matching},
language = {eng},
number = {1},
pages = {49-55},
title = {A Note on the Uniqueness of Stable Marriage Matching},
url = {http://eudml.org/doc/267608},
volume = {33},
year = {2013},
}

TY - JOUR
AU - Ewa Drgas-Burchardt
TI - A Note on the Uniqueness of Stable Marriage Matching
JO - Discussiones Mathematicae Graph Theory
PY - 2013
VL - 33
IS - 1
SP - 49
EP - 55
AB - In this note we present some sufficient conditions for the uniqueness of a stable matching in the Gale-Shapley marriage classical model of even size. We also state the result on the existence of exactly two stable matchings in the marriage problem of odd size with the same conditions.
LA - eng
KW - stable matching; Gale-Shapley model; stable perfect matching
UR - http://eudml.org/doc/267608
ER -

References

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  1. [1] E. Drgas-Burchardt and Z. Świtalski, A number of stable matchings in models of the Gale-Shapley type, manuscript.[WoS] Zbl1285.91101
  2. [2] J. Eeckhout, On the uniqueness of stable marriage matchings, Econom. Lett. 69 (2000) 1-8. doi:10.1016/S0165-1765(00)00263-9[WoS][Crossref] Zbl0960.91052
  3. [3] D. Gale, The two-sided matching problem: origin, development and current issues, Int. Game Theory Rev. 3 (2001) 237-252. doi:10.1142/S0219198901000373[Crossref] Zbl1127.91372
  4. [4] D. Gale and L.S. Shapley, College admissions and the stability of marriage, Amer. Math. Monthly 69 (1962) 9-15. doi:10.2307/2312726[Crossref] Zbl0109.24403
  5. [5] R.W. Irving and P. Leather, The complexity of counting stable marriages, SIAM J. Comput. 15 (1986) 655-667. doi:10.1137/0215048[Crossref] Zbl0611.68015
  6. [6] D.E. Knuth, Mariages Stables (Less Presses de l’Universite de Montreal, Montreal, 1976). 
  7. [7] D.E. Knuth, Stable Marriage and Its Relation to other Combinatorial Problems. An Introduction to the Mathematical Analysis of Algorithms (American Mathematical Society, Providence, Rhode Island, 1997). 

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