240:
methods from finite to infinite graphs: if the vertices of a graph can be well-ordered so that each vertex has few earlier neighbors, it has low chromatic number. When every finite subgraph has an ordering of this type in which the number of previous neighbors is at most
525:
187:
with Δ + 1 colors in such a way that the sizes of the color classes differ by at most one. Several authors have subsequently published simplifications and generalizations of this result.
703:. They first established the existence of Hausdorff spaces which are hereditarily separable, but not hereditarily Lindelöf, or vice versa. The existence of regular spaces with these properties (
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In 1992, Hajnal was awarded the
Officer's Cross of the Order of the Republic of Hungary. In 1999, a conference in honor of his 70th birthday was held at
785:
84:, and he remained there as a professor until his retirement in 2004. He became a member of the Hungarian Academy of Sciences in 1982, and directed its
885:
for the 2001 conference in honor of Hajnal and Sós calls him “the great chess player”; the conference included a blitz chess tournament in his honor.
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characterizes the graphs of this type with the maximum number of edges; Erdős, Hajnal and Moon find a similar characterization of the smallest
1649:
1617:
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Baumgartner, J. E.; Hajnal, A. (1987), "A remark on partition relations for infinite ordinals with an application to finite combinatorics",
89:
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vertices into finitely many subsets, at least one of the subsets contains a complete subgraph on α vertices, for every α < ω
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696:
326:; more specifically, all subsets' cardinalities should be smaller than some upper bound that is itself smaller than the cardinality of
58:
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and sufficiently large infinite chromatic number and the existence of graphs with high odd girth and infinite chromatic number.
256: − 2 earlier neighbors per vertex. The paper also proves the nonexistence of infinite graphs with high finite
92:
from 1980 to 1990, and president of the society from 1990 to 1994. Starting in 1981, he was an advisory editor of the journal
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34:
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An example of two graphs each with uncountable chromatic number, but with countably chromatic direct product. That is,
708:
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Kierstead, H. A.; Kostochka, A. V. (2008), "A short proof of the Hajnal–Szemerédi theorem on equitable colouring",
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866:. The 1957 date is from Hajnal's cv; the mathematics genealogy site lists the date of Hajnal's Ph.D. as 1956.
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1477:. For additional results of Baumgartner and Hajnal on partition relations, see the following two papers:
935:
Hajnal, A.; Maass, W.; Pudlak, P.; Szegedy, M.; Turán, G. (1987), "Threshold circuits of bounded depth",
712:
152:, and György Turán, showing exponential lower bounds on the size of bounded-depth circuits with weighted
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69:
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635:
128:, he had the second largest number of joint papers, 56. With Peter Hamburger, he wrote a textbook,
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Baumgartner, J.; Hajnal, A. (1973), "A proof (involving Martin's axiom) of a partition relation",
109:
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A. Hajnal, I. Juhász: On hereditarily α-Lindelöf and hereditarily α-separable spaces,
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Hajnal, A. (1961), "On a consistency theorem connected with the generalized continuum problem",
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Martin, Ryan; Szemerédi, Endre (2008), "Quadripartite version of the Hajnal–Szemerédi theorem",
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of
Mathematical Science degree (roughly equivalent to Ph.D.) in 1957, under the supervision of
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Foreman, M.; Hajnal, A. (2003). "A partition relation for successors of large cardinals".
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1608:, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 58,
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98:. Hajnal was also one of the honorary presidents of the European Set Theory Society.
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1483:, Contemp. Math., vol. 65, Providence, RI: Amer. Math. Soc., pp. 157–167,
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Combinatorial theory and its applications, II (Proc. Colloq., Balatonfüred, 1969)
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Baumgartner, James E.; Hajnal, Andras (2001), "Polarized partition relations",
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Catlin, Paul A. (1980), "On the Hajnal–Szemerédi theorem on disjoint cliques",
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520:{\displaystyle 2^{\aleph _{\omega _{1}}}<\aleph _{(2^{\aleph _{1}})^{+}}.}
124:
Hajnal was the author of over 150 publications. Among the many co-authors of
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925:
According to citation counts from Google scholar, retrieved March 1, 2009.
946:
737:
732:, and a second conference honoring the 70th birthdays of both Hajnal and
318:. This work concerns functions ƒ that map the members of an infinite set
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10.1002/(SICI)1097-0118(199908)31:4<275::AID-JGT2>3.0.CO;2-F
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1644:, Bolyai Society Mathematical Studies, vol. 15, Springer-Verlag,
1197:; Hajnal, A. (1966), "On chromatic number of graphs and set-systems",
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More sets, graphs and numbers: a salute to Vera Sós and András Hajnal
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1606:
Set Theory: The Hajnal
Conference, October 15–17, 1999 DIMACS Center
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80:; in 1994, he moved to Rutgers University to become the director of
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Fischer, Eldar (1999), "Variants of the Hajnal–Szemerédi theorem",
64:
He received his university diploma (M.Sc. degree) in 1953 from the
190:
A paper with Erdős and J. W. Moon on graphs that avoid having any
102:
1297:
Hajnal, A. (1961–1962), "Proof of a conjecture of S. Ruziewicz",
29:(May 13, 1931 – July 30, 2016) was a professor of mathematics at
1333:
Hajnal, A. (1985), "The chromatic number of the product of two ℵ
209:-clique-free graphs, showing that they take the form of certain
783:
Rutgers
University Department of Mathematics – Emeritus Faculty
392:
he proved several results on systems of infinite sets having
938:
Proc. 28th Symp. Foundations of
Computer Science (FOCS 1987)
1385:; Hajnal, A. (1964), "On a property of families of sets",
1416:; Hajnal, A. (1975), "Inequalities for cardinal powers",
914:
List of collaborators of Erdős by number of joint papers
288:
is a subset of κ, then ZFC and 2 = κ hold in
252:), an infinite graph has a well-ordering with at most 2
140:). Some of his more well-cited research papers include
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Hajnal's web page at the
Hungarian academy of sciences
1144:(10), Mathematical Association of America: 1107–1110,
802:
Hungarian
Academy of Sciences, Section for Mathematics
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578:
449:
409:
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List of
Fellows of the American Mathematical Society
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neither of which belongs to the image of the other.
213:. This paper also proves a conjecture of Erdős and
88:from 1982 to 1992. He was general secretary of the
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618:
519:
429:
1388:Acta Mathematica Academiae Scientiarum Hungaricae
1256:Acta Mathematica Academiae Scientiarum Hungaricae
619:{\displaystyle \omega _{1}\to (\alpha )_{n}^{2}.}
554:, that for every partition of the vertices of a
1510:(2), Association for Symbolic Logic: 811–821,
1481:Logic and combinatorics (Arcata, Calif., 1985)
566:. This can be expressed using the notation of
156:gates that solve the problem of computing the
971:(1970), "Proof of a conjecture of P. Erdős",
268:In his dissertation he introduced the models
8:
1735:Fellows of the American Mathematical Society
1730:Members of the Hungarian Academy of Sciences
1588:Ann. Univ. Sci. Budapest. Eötvös Sect. Math.
677:{\displaystyle \kappa ^{+}\to (\alpha )^{2}}
842:A halmazelmélet huszadik századi "Hajnal A"
688: < Ω, where Ω <
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1044:Combinatorics, Probability and Computing
362:). This result greatly extends the case
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1745:21st-century Hungarian mathematicians
1740:20th-century Hungarian mathematicians
772:Remembering András Hajnal (1931-2016)
430:{\displaystyle \aleph _{\omega _{1}}}
16:For the Hungarian Olympic diver, see
7:
1750:21st-century American mathematicians
1710:20th-century American mathematicians
1337:chromatic graphs can be countable",
844:, M. Streho's interview with A. H.,
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533:This was the result which initiated
338:subset in which no pair of elements
975:, North-Holland, pp. 601–623,
132:(Cambridge University Press, 1999,
53:Hajnal was born on 13 May 1931, in
1127:; Hajnal, A.; Moon, J. W. (1964),
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314:, the solution to a conjecture of
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761:Announcement from Rényi Institute
232:problems for infinite graphs and
90:János Bolyai Mathematical Society
740:. Hajnal became a fellow of the
699:he published several results in
264:Other selected results include:
114:European College of Liberal Arts
550:he proved a result in infinite
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1610:American Mathematical Society
1504:The Journal of Symbolic Logic
1137:American Mathematical Monthly
864:Mathematics Genealogy Project
742:American Mathematical Society
711:) was much later settled, by
403:in which they proved that if
368:Kuratowski's free set theorem
280:), and proved that if κ is a
35:Hungarian Academy of Sciences
1679:Hajnal's web page at Rutgers
638:then the partition relation
312:Hajnal's set mapping theorem
217:on the number of edges in a
1604:Thomas, Simon, ed. (1999),
1129:"A problem in graph theory"
1766:
1715:Rutgers University faculty
1200:Acta Mathematica Hungarica
1104:10.1016/j.disc.2007.08.019
385:fails for infinite graphs.
15:
1566:10.1007/s00208-002-0323-7
1067:10.1017/S0963548307008619
278:relative constructibility
120:Research and publications
108:Hajnal was the father of
692:is a very large ordinal.
169:Hajnal–Szemerédi theorem
78:Eötvös Loránd University
66:Eötvös Loránd University
1489:10.1090/conm/065/891246
1465:10.4064/fm-78-3-193-203
1452:Fundamenta Mathematicae
1312:10.4064/fm-50-2-123-128
1015:Journal of Graph Theory
904:from Hajnal's web site.
807:March 11, 2009, at the
634:he proved that if κ is
383:Hedetniemi's conjecture
1594:(1968), 115–124.
900:July 16, 2010, at the
701:set-theoretic topology
678:
620:
548:James Earl Baumgartner
521:
431:
228:A paper with Erdős on
86:mathematical institute
37:known for his work in
23:Hungarian set theorist
1554:Mathematische Annalen
1418:Annals of Mathematics
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621:
522:
439:strong limit cardinal
432:
236:. This paper extends
112:, the co-dean of the
18:András Hajnal (diver)
1091:Discrete Mathematics
995:Utilitas Mathematica
947:10.1109/SFCS.1987.59
895:List of publications
736:was held in 2001 in
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576:
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330:. Hajnal shows that
322:to small subsets of
33:and a member of the
1634:Katona, Gyula O. H.
941:, pp. 99–110,
612:
568:partition relations
316:Stanisław Ruziewicz
304:and 2 = ℵ
148:with Maas, Pudlak,
101:Hajnal was an avid
1401:10.1007/BF02066676
1353:10.1007/BF02579376
1269:10.1007/BF02023921
1224:10.1007/BF02020444
881:2008-07-24 at the
788:2010-07-15 at the
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366: = 1 of
173:equitable coloring
146:circuit complexity
31:Rutgers University
1651:978-3-540-32377-8
1619:978-0-8218-2786-4
1420:, Second Series,
1098:(19): 4337–4360,
724:Awards and honors
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1700:1931 births
1299:Fund. Math.
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401:Fred Galvin
250:-degenerate
234:hypergraphs
144:A paper on
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394:property B
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223:domination
130:Set Theory
126:Paul Erdős
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