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Mycielski Family
Mycielski is a Polish surname. Notable people with the surname include: *Jan Mycielski (born 1932), Polish-American mathematician **The Mycielskian, a construction in graph theory **The Grötzsch graph, sometimes called the Mycielski graph or the Mycielski-Grötzsch graph *Ludwik Mycielski Ludwik Mycielski (13 April 1854, Warsaw – 6 January 1926) was a Polish politician, president of the National Council (Rada Narodowa) in 1913. References * Witold Jakóbczyk, ''Przetrwać na Wartą 1815-1914'', ''Dzieje narodu i państwa po ... (1854-1926), Polish politician * Zygmunt Mycielski (1907-1987), Polish composer and music critic See also * Dołęga-Mycielski, Polish noble family {{surname Polish-language surnames ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jan Mycielski
Jan Mycielski (born February 7, 1932 in Wiśniowa, Podkarpackie Voivodeship, Poland)Curriculum vitae from Mycielski's web site, retrieved 2010-03-10. is a Polish-American , a professor emeritus of mathematics at the . Academic career Mycielski received his Ph.D. in mathematics from the |
Mycielskian
In the mathematical area of graph theory, the Mycielskian or Mycielski graph of an undirected graph is a larger graph formed from it by a construction of . The construction preserves the property of being triangle-free but increases the chromatic number; by applying the construction repeatedly to a triangle-free starting graph, Mycielski showed that there exist triangle-free graphs with arbitrarily large chromatic number. Construction Let the ''n'' vertices of the given graph ''G'' be ''v''1, ''v''2, . . . , ''v''n. The Mycielski graph μ(''G'') contains ''G'' itself as a subgraph, together with ''n''+1 additional vertices: a vertex ''u''''i'' corresponding to each vertex ''v''''i'' of ''G'', and an extra vertex ''w''. Each vertex ''u''''i'' is connected by an edge to ''w'', so that these vertices form a subgraph in the form of a star ''K''1,''n''. In addition, for each edge ''v''''i''''v''''j'' of ''G'', the Mycielski graph includes two edges, ''u''''i''''v''''j'' and ''v''''i' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grötzsch Graph
In the mathematical field of graph theory, the Grötzsch graph is a triangle-free graph with 11 vertices, 20 edges, chromatic number 4, and crossing number 5. It is named after German mathematician Herbert Grötzsch, who used it as an example in connection with his 1959 theorem that planar triangle-free graphs are 3-colorable. The Grötzsch graph is a member of an infinite sequence of triangle-free graphs, each the Mycielskian of the previous graph in the sequence, starting from the one-edge graph; this sequence of graphs was constructed by to show that there exist triangle-free graphs with arbitrarily large chromatic number. Therefore, the Grötzsch graph is sometimes also called the Mycielski graph or the Mycielski–Grötzsch graph. Unlike later graphs in this sequence, the Grötzsch graph is the smallest triangle-free graph with its chromatic number. Properties The full automorphism group of the Grötzsch graph is isomorphic to the dihedral group D5 of order 10, the grou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ludwik Mycielski
Ludwik Mycielski (13 April 1854, Warsaw – 6 January 1926) was a Polish politician, president of the National Council (Rada Narodowa) in 1913. References * Witold Jakóbczyk, ''Przetrwać na Wartą 1815-1914'', ''Dzieje narodu i państwa polskiego'', vol. III-55, Krajowa Agencja Wydawnicza, Warszawa 1989 1854 births 1926 deaths Politicians from Warsaw People from Warsaw Governorate Ludwik Ludwik () is a Polish given name. Notable people with the name include: * Ludwik Czyżewski, Polish WWII general * Ludwik Fleck (1896–1961), Polish medical doctor and biologist * Ludwik Gintel (1899–1973), Polish-Israeli Olympic soccer playe ... Members of the 6th Reichstag of the German Empire Members of the 7th Reichstag of the German Empire Polish deputies to the Reichstag in Berlin {{Poland-politician-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zygmunt Mycielski
Count Zygmunt Mycielski (17 August 1907 – 5 August 1987) was a Polish composer and music critic. He was born in Przeworsk and completed his childhood education in Kraków, where he was taught by Bernardino Rizzi. In 1928, Mycielski moved to Paris, where he studied composition at École Normale de Musique with Paul Dukas and Nadia Boulanger. While there, he served as president of the Association of Young Polish Musicians in Paris from 1934 to 1936. In 1936, he moved back to Poland and began his music and writing career. Mycielski served in the Polish military during World War II and became a prisoner of war after being captured by the German Army. For the rest of the war, he did compulsory work for a German farmer. After the war ended, he returned to Poland and served two terms as editor for '' Ruch Muzyczny'' (1946–1948 and 1957–1959) before becoming editor-in-chief from 1960 to 1968. His political views clashed with communist Polish authorities, however. His publications c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
