A Note on the Uniqueness of Stable Marriage Matching

• Autorzy: Ewa Drgas-Burchardt
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

stable matching; Gale-Shapley model; stable perfect matching

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2013
• Tom: 33
• Numer: 1
• Strony: 49-55

Daty

wydano

2013-03-01

online

2013-04-13

Twórcy

autor

Ewa Drgas-Burchardt

• Faculty of Mathematics, Computer Science and Econometrics University of Zielona Góra ul. prof. Z.Szafrana 4a, 65-516 Zielona Góra, Poland

Bibliografia

• [1] E. Drgas-Burchardt and Z. Świtalski, A number of stable matchings in models of the Gale-Shapley type, manuscript.[WoS]
• [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]
• [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]
• [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]
• [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]
• [6] D.E. Knuth, Mariages Stables (Less Presses de l’Universite de Montreal, Montreal, 1976).
• [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).

Identyfikatory

DOI

10.7151/dmgt.1667