Brandstädt, A., Le, V., and Spinrad, J. (1999). Graph
Classes: A Survey. SIAM Monographs on Discrete
Mathematics and Applications.
Demange, M. and Ekim, T. (2008). Minimum maxi-
mal matching is NP-hard in regular bipartite graphs.
In TAMC 2008, Lecture Notes in Computer Science,
4978, pages 364–374.
Demange, M. and Ekim, T. (2013). A note on the NP-
hardness of two matching problems in induced sub-
grids. Discrete Mathematics and Theoretical Com-
puter Science, 15(2):233–242.
Demange, M. and Ekim, T. (2014). Efficient recognition of
equimatchable graphs. Information Processing Let-
ters, 114:66–71.
Dibek, C., Ekim, T., Gözüpek, D., and Shalom, M. (2016).
Equimatchable graphs are C
2k+1
-free for k ≤ 4. Dis-
crete Mathematics, 339:2964–2969.
Eiben, E. and Kotrb
ˇ
cík, M. (2015). Equimatchable factor-
critical graphs and independence number 2. arXiv
preprint arXiv:1501.07549.
Favaron, O. (1986). Equimatchable factor-critical graphs.
Journal of Graph Theory, 10(4):439–448.
Gale, D. and Shapley, L. (1962). College admissions and
the stability of marriage. American Mathematical
Monthly, 69:9–15.
Gale, D. and Sotomayor, M. (1985). Some remarks on the
stable matching problem. Discrete Applied Mathemat-
ics, 11:223–232.
Garey, M. R. and Johnson, D. S. (1979). Computers
and Intractability - A Guide to the Theory of NP-
completeness. Freeman.
Golumbic, M. C. (2004). Algorithmic Graph Theory and
Perfect Graphs. Annals of Discrete Mathematics 57.
Grünbaum, B. (1974). Matchings in polytopal graphs. Net-
works, 4:175–190.
Horton, J. and Kilakos, K. (1993). Minimum edge domi-
nating sets. SIAM Journal on Discrete Mathematics,
6(3):375–387.
http://www.graphclasses.org/ (2019).
Hwang, S. and Chang, G. (1995). The edge domination
problem. Discuss. Math. Graph. Theory, 15(1):51–
57.
Iwama, K. and Miyazaki, S. (2008). A survey of the sta-
ble marriage problem and its variants. In Int. Conf.
Informatics Education and Research for Knowledge-
Circulating Society, pages 131–136.
Lesk, M., Plummer, M. D., and Pulleyblank, W. R. (1984).
Equi-matchable graphs. In Graph Theory and Com-
binatorics (Cambridge, 1983), pages 239–254. Aca-
demic Press, London.
Lewin, M. (1974). Matching-perfect and cover-perfect
graphs. Israel Journal of Mathematics, 18:345–347.
Meng, D. H.-C. (1974). Matchings and Coverings for
Graphs. PhD thesis, Michigan State University, East
Lansing, MI.
Mitchell, S. and Hedetniemi, S. (1977). Edge domination in
trees. In Proceedings of the 8th Southeastern Confer-
ence on Combinatorics, Graph Theory and Comput-
ing, pages 489–509, Louisiana State University, Baton
Rouge, La.
Plummer, M. D. and Lovász, L. (1986). Matching Theory.
Annals of Discrete Mathematics 29.
Richey, M. and Parker, R. (1988). Minimum-maximal
matching in series-parallel graphs. European Journal
of Operations Research, 33(1):98–105.
Roth, A. (1982). The economics of matching: Stability
and incentives. Mathematics of Operations Research,
7:617–628.
Roth, A. (1984). Misrepresentation and stability in the mar-
riage problem. Journal of Economic Theory, 34:383–
387.
Roth, A. (2008). Deferred acceptance algorithms: history,
theory, practice and open questions. Int. J. Game The-
ory, 36:537–569.
Roth, A., Sönmez, T., and Ünver, M. U. (2004). Kidney
exchange. Quarterly Journal of Economics, 119:457–
488.
Roth, A., Sönmez, T., and Ünver, M. U. (2015). Pair-
wise kidney exchange. Journal of Economic Theory,
125:151 – 188.
Roth, A. E. (2012). Random graph models in kidney ex-
change - theoretical developments and practical chal-
lenges (the movie).
Roth, A. E. (2016). Who Gets What â
˘
A¸T and Why: The
New Economics of Matchmaking and Market Design.
Eamon Dolan/Mariner Books.
Sciences Prize Committee of the Royal Swedish
Academy of Science, E. (2012). Scientific Back-
ground on the Sveriges Riksbank Prize in Economic
Sciences in Memory of Alfred Nobel 2012.
Srinivasan, A., Madhukar, K., Nagavamsi, P., Rangan, C. P.,
and Chang, M.-S. (1995). Edge domination on bipar-
tite permutation graphs and cotriangulated graphs. In-
formation Processing Letters, 56(3):165–171.
Toulis, P. and Parkes, D. (2011). A random graph model
of kidney exchanges: efficiency, individual-rationality
and incentives. In EC’11 Proceedings of the 12th
ACM conference on Electronic commerce, pages 323–
332. ACM New York.
Yannakakis, M. and Gavril, F. (1980). Edge dominating
sets in graphs. SIAM Journal on Applied Mathematics,
38:364–372.
ICORES 2020 - 9th International Conference on Operations Research and Enterprise Systems
16