Jan Mycielski is a Polish-American mathematician, a professor emeritus of mathematics at the University of Colorado at Boulder

University of Colorado at Boulder

The University of Colorado Boulder is a public research university located in Boulder, Colorado...

.

Mycielski received his Ph.D. in mathematics from the University of Wrocław in 1957 under the supervision of Stanisław Hartman. Following positions at the Centre National de la Recherche Scientifique

Centre national de la recherche scientifique

The National Center of Scientific Research is the largest governmental research organization in France and the largest fundamental science agency in Europe....

 in Paris

Paris

Paris is the capital and largest city in France, situated on the river Seine, in northern France, at the heart of the Île-de-France region...

, the Institute of Mathematics of the Polish Academy of Sciences

Polish Academy of Sciences

The Polish Academy of Sciences, headquartered in Warsaw, is one of two Polish institutions having the nature of an academy of sciences.-History:...

, the University of California, Berkeley

University of California, Berkeley

The University of California, Berkeley , is a teaching and research university established in 1868 and located in Berkeley, California, USA...

, and Case Western Reserve University

Case Western Reserve University

Case Western Reserve University is a private research university located in Cleveland, Ohio, USA...

, he took a permanent faculty position at Colorado in 1969.

Among the mathematical concepts named after Mycielski are:

• The Ehrenfeucht–Mycielski sequence
  Ehrenfeucht–Mycielski sequence
  The Ehrenfeucht–Mycielski sequence is a recursively defined sequence of binary digits with pseudorandom properties, defined by .-Definition:The sequence starts with the three bits 010; each successive digit is formed by finding the longest suffix of the sequence that also appears earlier within the...
  
  , a sequence of binary digits with pseudorandom properties
• The Mycielskian
  Mycielskian
  In the mathematical area of graph theory, the Mycielskian or Mycielski graph of an undirected graph G is a graph μ formed from G by a construction of , who used it to show that there exist triangle-free graphs with arbitrarily large chromatic number.-Construction:Let the n vertices of the given...
  
  , a construction for embedding any undirected graph into a larger graph with higher chromatic number without creating any additional triangles.
• The Mycielski–Grötzsch graph
  Grötzsch graph
  In the mathematical field of graph theory, the Grötzsch graph is a triangle-free graph with 11 vertices, 20 edges, and chromatic number 4. It is named after German mathematician Herbert Grötzsch, and its existence demonstrates that the assumption of planarity is necessary in Grötzsch's theorem ...
  
  , the Mycielskian of the 5-cycle, an 11-vertex triangle-free graph
  Triangle-free graph
  In the mathematical area of graph theory, a triangle-free graph is an undirected graph in which no three vertices form a triangle of edges. Triangle-free graphs may be equivalently defined as graphs with clique number ≤ 2, graphs with girth ≥ 4, graphs with no induced 3-cycle, or locally...
  
   that is the smallest possible triangle-free graph requiring four colors.
• Mycielski's theorem that there exist triangle-free graphs with arbitrarily large chromatic number.

External links

• Mycielski's personal web page at the Univ. of Colorado.