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German-American mathematician
Gerhard Ringel (October 28, 1919 in Kollnbrunn, Austria – June 24, 2008 in Santa Cruz, California) was a German mathematician. He was one of the pioneers
Gerhard_Ringel
Theorem on graph coloring on surfaces
conjecture was formulated in 1890 by P.J. Heawood and proven in 1968 by Gerhard Ringel and J.W.T. Youngs. One case, the non-orientable Klein bottle, proved
Heawood_conjecture
Surname
prevention Faye Ringel, former American professor of humanities at the United States Coast Guard Academy and an author Gerhard Ringel (1919–2008), German
Ringel
Type of graph vertex labeling
graph theory is the graceful tree conjecture or Ringel–Kotzig conjecture, named after Gerhard Ringel and Anton Kotzig, and sometimes abbreviated GTC (not
Graceful_labeling
Unsolved problem on graph coloring
coloring problem (solved by the four color theorem), and was posed by Gerhard Ringel in 1959. An intuitive form of the problem asks how many colors are needed
Earth–Moon_problem
German mathematician (1905–1980)
explicit use of homology. Sperner's students included Kurt Leichtweiss and Gerhard Ringel. Ein Satz über Untermengen einer endlichen Menge. Math. Z. 27 (1928)
Emanuel_Sperner
Unsolved problem in graph theory
Research Institute for Mathematics, where the problem was posed in 1967 by Gerhard Ringel. It is known to be true for all sufficiently large complete graphs.
Oberwolfach_problem
Planar maps require at most four colors
Heawood in 1890 and, after contributions by several people, proved by Gerhard Ringel and J. W. T. Youngs in 1968. The only exception to the formula is the
Four_color_theorem
conjectures (now theorems). Bernhard Riemann 24900 Ringel–Kotzig conjecture graph theory Gerhard Ringel and Anton Kotzig 187 Rudin's conjecture additive
List_of_conjectures
1990 book by Gerhard Ringel and Nora Hartsfield
undergraduate-level textbook on graph theory by Nora Hartsfield and Gerhard Ringel. It was published in 1990 by Academic Press with a revised edition in
Pearls_in_Graph_Theory
Number of planar subgraphs to cover a graph
problem on the chromatic number of biplanar graphs, posed in 1959 by Gerhard Ringel, and on a related 1962 conjecture of Frank Harary: Every graph on nine
Thickness_(graph_theory)
Slovak-Canadian mathematician
are named after him. These include the Ringel–Kotzig conjecture on graceful labeling of trees (with Gerhard Ringel); Kotzig's conjecture on regularly path
Anton_Kotzig
Combinatorial representation of a graph on an orientable surface
the concept was already extensively used under the name "rotation" by Gerhard Ringel and J.W.T. Youngs in their famous solution of the Heawood map-coloring
Combinatorial_map
Upper bound for number of colors that suffice to color any graph
never exceeds 6 {\displaystyle 6} . Later it was proved in the works of Gerhard Ringel, J. W. T. Youngs, and other contributors that the complete graph with
Heawood_number
British mathematician (1916–2020)
Berlekamp, John L. Selfridge, Kenneth Falconer, Frank Harary, Lee Sallows, Gerhard Ringel, Béla Bollobás, C. B. Lacampagne, Bruce Sagan, and Neil Sloane. Over
Richard_K._Guy
Reingold Jennifer Rexford Dana S. Richards Frigyes Riesz John Rigby Gerhard Ringel Alexander Rinnooy Kan John Riordan Jorma Rissanen Ivan Rival Ron Rivest
List of people by Erdős number
List_of_people_by_Erdős_number
On minimizing crossings in bicliques
discovered until eleven years after publication, nearly simultaneously by Gerhard Ringel and Paul Kainen. Nevertheless, it is conjectured that Zarankiewicz's
Turán's_brick_factory_problem
Municipality in Lower Austria, Austria
17 percent of the municipality is forested. Bad Pirawarth Kollnbrunn Gerhard Ringel, born at Kollnbrunn "Dauersiedlungsraum der Gemeinden Politischen Bezirke
Bad_Pirawarth
Day of the year
Derek Dougan, Northern Irish footballer and manager (born 1938) 2008 – Gerhard Ringel, Austrian mathematician and academic (born 1919) 2009 – Roméo LeBlanc
June_24
Richarz Eugen Richter Hans Riegel Charles Pierre Henri Rieu Matthias Ring Gerhard Ringel Albrecht Ritschl Otto Ritschl Franz Ritter Emil Ritterling Robert Kurt
List of University of Bonn people
List_of_University_of_Bonn_people
Book on graph coloring and Ramsey theory
the proof of the Heawood conjecture on coloring graphs on surfaces by Gerhard Ringel and Ted Youngs. And Günter M. Ziegler complains that many claims are
The Mathematical Coloring Book
The_Mathematical_Coloring_Book
American mathematician
problem for Frechét Surfaces, Memoirs American Mathematical Society 1951 Ringel, Gerhard; Youngs, J.W.T. (1968). "Solution of the Heawood map-coloring problem"
John_William_Theodore_Youngs
British mathematician
same authors proved Ringel's conjecture for all sufficiently large n {\displaystyle n} . The conjecture, posed by Gerhard Ringel in 1963, states that
Richard Montgomery (mathematician)
Richard_Montgomery_(mathematician)
German painter (born 1969)
with Robert Adams), Galerie Thomas Zander, Köln; Lagune, Galerie Felix Ringel, Düsseldorf; Journal Entries, Heni Publishing, London 2019: deeply unaware
Sabine_Moritz
magic square is semimagic, but not vice versa. Nora Hartsfield and Gerhard Ringel (1994, 2003), Pearls in Graph Theory, revised edition. Dover Publications
Magic_graph
Toroidal polyhedron with 7 faces
71 (4): 1429–1455, doi:10.1007/S00454-023-00537-6 Jungerman, M.; Ringel, Gerhard (1980), "Minimal triangulations on orientable surfaces", Acta Mathematica
Szilassi_polyhedron
National association football team
"natives" anyway as some had joined Saarland clubs from elsewhere, like Ringel, Immig or goalkeepers Borcherding and Jirasek; see List of Saarland international
Saarland national football team
Saarland_national_football_team
American businessman and scientist
molecule with a grant from the National Institutes of Health. For Dr. Gerhard Ringel, head of the Math department at UCSC, Risan worked on embeddings on
Hank_Risan
Graph with at most one crossing per edge
minimal number of edges that must be removed to make a graph planar. Ringel, Gerhard (1965), "Ein Sechsfarbenproblem auf der Kugel", Abhandlungen aus dem
1-planar_graph
Regular graph with fewest possible nodes for its girth
original (PDF) on 2016-03-09, retrieved 2010-02-23. Hartsfield, Nora; Ringel, Gerhard (1990), Pearls in Graph Theory: A Comprehensive Introduction, Academic
Cage_(graph_theory)
Subgraph induced by all nodes linked to a given node of a graph
39 (1): 3–6, hdl:10338.dmlcz/136481, MR 1016323 Hartsfeld, Nora; Ringel, Gerhard (1991), "Clean triangulations", Combinatorica, 11 (2): 145–155, doi:10
Neighbourhood_(graph_theory)
Defunct cultural and political magazine in Austria (1954–1995)
1954 to 1965. In 1965 Günther Nenning took over as editor and in 1986 Gerhard Oberschlick. The magazine was distributed internationally and instigated
FORVM
Type of machine learning model
18653/v1/2023.emnlp-main.507. Park, Joon Sung; O'Brien, Joseph C.; Cai, Carrie J.; Ringel Morris, Meredith; Liang, Percy; Bernstein, Michael S. (1 April 2023). Generative
Large_language_model
Abstract simplicial complex describing a graph's cliques
Journal of Combinatorics, 9 R17, doi:10.37236/1634. Hartsfeld, N.; Ringel, Gerhard (1991), "Clean triangulations", Combinatorica, 11 (2): 145–155, doi:10
Clique_complex
On graph drawing with integer edge lengths
integer-distance realization problem in three dimensions Hartsfield, Nora; Ringel, Gerhard (2013), Pearls in Graph Theory: A Comprehensive Introduction, Dover
Harborth's_conjecture
World War II German military unit
the town of Santhià, on the way to Milan, resulting in 48 deaths. Julius Ringel (1 November 1940 – 10 February 1944) Max-Günther Schrank (10 February 1944
5th Mountain Division (Wehrmacht)
5th_Mountain_Division_(Wehrmacht)
Momber 1 10 0.10 Robert Niederkirchner 1 1 1.00 Werner Otto 1 6 0.17 Karl Ringel 1 2 0.50 Two goalkeepers managed to keep a clean sheet in Saarland's nineteen
Saarland national football team records and statistics
Saarland_national_football_team_records_and_statistics
2017. Archived from the original on May 4, 2017. Retrieved May 1, 2017. Ringel, Jonathan (November 4, 2018). "Updated: Former Chief Justice Harris Hines
List of people who died in traffic collisions
List_of_people_who_died_in_traffic_collisions
Saarland. Franz Immig had already played for Germany in 1939, while Karl Ringel, Gerhard Siedl and Heinz Vollmar did so in later years. Player This colour
List of Saarland international footballers
List_of_Saarland_international_footballers
1007/s00493-004-0015-x. MR 2071334. S2CID 46133408. Hartsfield, Nora; Ringel, Gerhard (2013). Pearls in Graph Theory: A Comprehensive Introduction. Dover
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Football match
27 December 1959 (1959-12-27) 13:45 CET Auestadion, Kassel Attendance: 20,000 Referee: Gerhard Schulenburg (Hamburg) "Schiedsrichter: Der erste war Berliner". DFB-Pokal:
1959_DFB-Pokal_final
Germany: Scherzers Miltaer-Verlag. ISBN 978-3-938845-17-2. Von Seemen, Gerhard (1976). Die Ritterkreuzträger 1939–1945 : die Ritterkreuzträger sämtlicher
List of Knight's Cross of the Iron Cross recipients (R)
List_of_Knight's_Cross_of_the_Iron_Cross_recipients_(R)
Association football club in Germany
DFB-Pokal final to Bayern Munich on penalties, Lothar Matthäus and Norbert Ringels both missing from the spot after the game originally ended all square at
Borussia_Mönchengladbach
Pogorelov M. J. D. Powell Michael O. Rabin Kenneth Alan Ribet Claus Michael Ringel R. T. Rockafellar David Ruelle Mikio Sato Wolfgang M. Schmidt Richard M
List of International Congresses of Mathematicians Plenary and Invited Speakers
List_of_International_Congresses_of_Mathematicians_Plenary_and_Invited_Speakers
2008 film
Campino as Finn Inga Busch as Karla Axel Sichrovsky as Hans Gerhard Gutberlet as Gerhard Harry Blain as Harry Sebastian Blomberg as Julian Jana Pallaske
Palermo_Shooting
Players of Germany's national football team
Three of the Saar team's players later represented Germany: Karl Ringel, Gerhard Siedl and Heinz Vollmar. Upon Germany's reunification in 1990, the
List of Germany international footballers
List_of_Germany_international_footballers
Central text of Rabbinic Judaism
Hirschberg, A History of the Jews in North Africa, pp. 125–126. Joseph Ringel, "A Third Way: Iyyun Tunisai as a Traditional Critical Method of Talmud
Talmud
1938 annexation of Austria into Nazi Germany
Erhard Raus Hanns Albin Rauter Anton Reinthaller Lothar Rendulic Julius Ringel Arthur Seyss-Inquart Otto Skorzeny Otto Wächter Mauritz von Wiktorin Alois
Anschluss
Tree which includes all vertices of a graph
University Press, p. 141, ISBN 978-0-19-920250-8. Hartsfield, Nora; Ringel, Gerhard (2003), Pearls in Graph Theory: A Comprehensive Introduction, Courier
Spanning_tree
Axis invasion of Crete during World War II
anti-tank unit, a motorised artillery troop, and some engineers. General Ringel gave orders for Wittmann to "strike out from Platanos at 03:00 on 28 May
Battle_of_Crete
Graph formed by touching unit circles
(PDF), Geombinatorics, 19 (1): 28–30, MR 2584434 Hartsfield, Nora; Ringel, Gerhard (2013), "Problem 8.4.8", Pearls in Graph Theory: A Comprehensive Introduction
Penny_graph
German music festival
1978: Gerhard Klingenberg 1979: Werner Hofmann 1980: Ernst Krenek 1981: Anton Neumayr 1982: Rolf Liebermann 1983: Fritz Hochwälder 1984: Erwin Ringel 1985:
Brucknerfest
Football tournament season
Neunkirchen 5 – 2. 16 August 1959 Poststadion, Berlin Attendance: 8.000 Referee: Gerhard Schulenburg (Hamburg) 3 October 1959 Ellenfeldstadion, Neunkirchen Attendance:
1958–59_DFB-Pokal
Kenyan Roman Catholic prelate, bishop of Francistown (since 2021). Karl Ringel, 91, German footballer (Borussia Neunkirchen, Saarland national team, West
Deaths_in_May_2024
Battle of World War II
progress against the German 5th Mountain Division, commanded by General Julius Ringel, gaining positions on the slopes of their key objective, Monte Cifalco.
Battle_of_Monte_Cassino
British film industry award
Denis Villeneuve, Luc Déry, Kim McCraw Canada Pina Wim Wenders, Gian-Piero Ringel Germany Potiche François Ozon, Eric Altmeyer, Nicolas Altmeyer France A
BAFTA Award for Best Film Not in the English Language
BAFTA_Award_for_Best_Film_Not_in_the_English_Language
Marcus Vetter, Leon Geller 2011 Pina Wim Wenders, Gian-Piero Ringel Wim Wenders 2012 Gerhard Richter Painting Thomas Kufus Corinna Belz 2013 More than Honey
German Film Award for Best Documentary Film
German_Film_Award_for_Best_Documentary_Film
Leipzig: Leipziger Universitätsverlag, pp. 525f., ISBN 978-3-86583-804-9 Ringel, Sebastian (2015). Leipzig! One Thousand Years of History. Leipzig: Author
Leipzig_Beat_Revolt
Fewest edge crossings in drawing of a graph
(1): 1–14. doi:10.1007/s00454-007-1325-8. Retrieved 22 July 2025. Ringel, Gerhard (1965). "Ein Sechsfarbenproblem auf der Kugel". Abhandlungen aus dem
Crossing number (graph theory)
Crossing_number_(graph_theory)
Quality of zero being an even number
Discourse, Walter de Gruyter, ISBN 978-90-279-3164-1 Hartsfield, Nora; Ringel, Gerhard (2003), Pearls in Graph Theory: A Comprehensive Introduction, Mineola
Parity_of_zero
Computer science research award
Jean-Daniel Fekete, Jason Hong, Kristina Höök, Kasper Hornbæk, Meredith Ringel Morris, Peter Wright 2021 Maneesh Agrawala, Ann Blandford, Jeffrey Heer
CHI_Academy
Overview of all Volkskammer members
Vertreterin Luise Ermisch SED Arno Ettrich SED am 16. November 1956 für den Abg. Ringel nachgerückt Theodor Eversmann CDU am 2. November 1956 für die Abg. Olbrich
List of members of the second Volkskammer
List_of_members_of_the_second_Volkskammer
Flat-sided three-dimensional shape
Patterns and Symmetry, Dover Publications, p. 134, ISBN 978-0-486-83654-6 Ringel, Gerhard (1974), "Classification of surfaces", Map Color Theorem, Springer,
Polyhedron
Overview of the architecture in Leipzig
Architekturführer: die 100 wichtigsten Leipziger Bauwerke, Berlin: Jaron, OCLC 774688985 Ringel, Sebastian (2015). Leipzig! One Thousand Years of History. Leipzig: Author
Architecture_of_Leipzig
Richard Richter DBD on July 23, 1952, announcement of loss of mandate Otto Ringel SED moved up on July 30, 1953 Paul Roch DBD Herbert Roepke SED Wolfgang
List of members of the first Volkskammer
List_of_members_of_the_first_Volkskammer
Maltz Volker Markl Maja Matarić Filippo Menczer Jose Meseguer Meredith Ringel Morris Nachiappan Nagappan Radhika Nagpal Moni Naor Chandrasekhar Narayanaswami
List of fellows of the Association for Computing Machinery
List_of_fellows_of_the_Association_for_Computing_Machinery
German-American composer and filmmaker (born 1961)
Henning Lohner: Gerhard Richter im Atelier, Stiftung Brandenburger Tor – Max Liebermann Haus, Berlin 2018: Galerie Hus, Paris 2017: Felix Ringel Galerie, Düsseldorf
Henning_Lohner
Commander of the I./Grenadier-Regiment 176 14 October 1943 — — 312 Julius Ringel Heer 19-HGeneralleutnant Commander of 5. Gebirgs-Division 25 October 1943
List of Knight's Cross of the Iron Cross with Oak Leaves recipients (1943)
List_of_Knight's_Cross_of_the_Iron_Cross_with_Oak_Leaves_recipients_(1943)
9th season of Europe's secondary club football tournament organised by UEFA
Attendance: 9,800 Referee: Dušan Krchňák (Czechoslovakia) 19 September 1979 Gerhard Hanappi Stadium, Vienna Attendance: 12,000 Referee: Paolo Casarin (Italy)
1979–80_UEFA_Cup
Austrian award
accident and was severely injured in the process) Stefan Jellinek Erwin Ringel Hans Rotter (secretary in association Trinkerheilstätte) Gesellschaft der
Karl_Renner_Prize
bacteriology and immunology Wilhelm Reich (1897–1957), psychiatrist Erwin Ringel (1921–1994), Austrian psychiatrist (presuicidal syndrome) Ignaz Semmelweis
List_of_Austrians
1925 opera by Alban Berg; Berg's first opera
Die Fackel [de] by 1916. Marie's orphan plays among children singing "Ringel, Ringel, Rosenkranz, Ringelreih'n" (like "Ring a Ring o' Roses") in the epilogue
Wozzeck
Julius Ringel Karl Ritter Karl Ritter (director) Carl-Heinz Rodenberg Arthur Rödl Walter Rohland Ernst Röhm Karl von Roques Eduard Roschmann Gerhard Rose
List_of_Nazis_(L–R)
Solid with eight equal triangular faces
1007/978-3-319-30451-9_12. ISBN 978-3-319-30451-9. Hartsfield, Nora; Ringel, Gerhard (2003). Pearls in Graph Theory: A Comprehensive Introduction. Dover
Regular_octahedron
German historian
Autorität. Von Rom 1111 bis Venedig 1177. In: Ernst-Dieter_Hehl, Ingrid Heike Ringel, Hubertus Seibert (Hrsg.): Das Papsttum in der Welt des 12. Jahrhunderts
Stefan_Weinfurter
Chemical compound
1152/ajpendo.00508.2010. PMID 20858748. S2CID 6062445. Ramsden, Christopher E; Ringel, Amit; Feldstein, Ariel E; Taha, Ameer Y; MacIntosh, Beth A; Hibbeln, Joseph
13-Hydroxyoctadecadienoic acid
13-Hydroxyoctadecadienoic_acid
Award
- Steve James Outstanding Achievement in Production - Pina - Gian-Piero Ringel, Wim Wenders Outstanding Achievement in Cinematography - Hell and Back Again
Cinema_Eye_Honors
Players of the Germany national football team with 5 to 19 caps
available in German) Sascha Riether at DFB (also available in German) Karl Ringel at DFB (also available in German) Hans Riso at DFB (also available in German)
List of Germany international footballers (1–4 caps)
List_of_Germany_international_footballers_(1–4_caps)
Kurfürstentums Sachsen. Typenkatalog albertinische Linie 1546–1763. Leipzig. Krug, Gerhard (1974). Die meißnisch-sächsischen Groschen 1338–1500. Berlin. Lorenz, Rudolf
Coinage_of_Saxony
Artist duo
Henning Lohner: Gerhard Richter im Atelier, Stiftung Brandenburger Tor – Max Liebermann Haus, Berlin 2018: Galerie Hus, Paris 2017: Felix Ringel Galerie, Düsseldorf
Lohner_Carlson
GERHARD RINGEL
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