Robin Thomas (mathematician)

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Robin Thomas
Born(1962-08-22)August 22, 1962 [1]
Prague, Czechoslovakia
DiedMarch 26, 2020(2020-03-26) (aged 57) [2]
Alma mater Charles University
Awards Fulkerson Prize
Karel Janeček Foundation Neuron Prize
Scientific career
Fields Mathematics
Institutions Georgia Institute of Technology
Doctoral advisor Jaroslav Nešetřil

Robin Thomas (August 22, 1962 – March 26, 2020) was a mathematician working in graph theory at the Georgia Institute of Technology.

Contents

Thomas received his doctorate in 1985 from Charles University in Prague, Czechoslovakia (now the Czech Republic), under the supervision of Jaroslav Nešetřil. [3] He joined the faculty at Georgia Tech in 1989, and became a Regents' Professor there, [4] [5] briefly serving as the department Chair.

On March 26, 2020, he lost his twelve-year struggle against Amyotrophic Lateral Sclerosis at the age of 57. [2] [6]

Awards

Thomas was awarded the Fulkerson Prize for outstanding papers in discrete mathematics twice, [7] in 1994 as co-author of a paper on the Hadwiger conjecture, [8] and in 2009 for the proof of the strong perfect graph theorem. [9] In 2011 he was awarded the Karel Janeček Foundation Neuron Prize for Lifetime Achievement in Mathematics. [10] In 2012 he became a fellow of the American Mathematical Society. [11] He was named a SIAM Fellow in 2018. [12]

Related Research Articles

In graph theory, an undirected graph H is called a minor of the graph G if H can be formed from G by deleting edges and vertices and by contracting edges.

In graph theory, the perfect graph theorem of László Lovász states that an undirected graph is perfect if and only if its complement graph is also perfect. This result had been conjectured by Berge, and it is sometimes called the weak perfect graph theorem to distinguish it from the strong perfect graph theorem characterizing perfect graphs by their forbidden induced subgraphs.

Snark (graph theory)

In the mathematical field of graph theory, a snark is a simple, connected, bridgeless cubic graph with chromatic index equal to 4. In other words, it is a graph in which every vertex has three neighbors, the connectivity is redundant so that removing no one edge would split the graph, and the edges cannot be colored by only three colors without two edges of the same color meeting at a point. In order to avoid trivial cases, snarks are often restricted to have girth at least 5.

In graph theory, the strong perfect graph theorem is a forbidden graph characterization of the perfect graphs as being exactly the graphs that have neither odd holes nor odd antiholes. It was conjectured by Claude Berge in 1961. A proof by Maria Chudnovsky, Neil Robertson, Paul Seymour, and Robin Thomas was announced in 2002 and published by them in 2006.

In topological graph theory, a mathematical discipline, a linkless embedding of an undirected graph is an embedding of the graph into three-dimensional Euclidean space in such a way that no two cycles of the graph are linked. A flat embedding is an embedding with the property that every cycle is the boundary of a topological disk whose interior is disjoint from the graph. A linklessly embeddable graph is a graph that has a linkless or flat embedding; these graphs form a three-dimensional analogue of the planar graphs. Complementarily, an intrinsically linked graph is a graph that does not have a linkless embedding.

The Fulkerson Prize for outstanding papers in the area of discrete mathematics is sponsored jointly by the Mathematical Optimization Society (MOS) and the American Mathematical Society (AMS). Up to three awards of $1,500 each are presented at each (triennial) International Symposium of the MOS. Originally, the prizes were paid out of a memorial fund administered by the AMS that was established by friends of the late Delbert Ray Fulkerson to encourage mathematical excellence in the fields of research exemplified by his work. The prizes are now funded by an endowment administered by MPS.

George Neil Robertson is a mathematician working mainly in topological graph theory, currently a distinguished professor emeritus at the Ohio State University. He earned his B.Sc. from Brandon College in 1959, and his Ph.D. in 1969 at the University of Waterloo under his doctoral advisor William Tutte.

Paul Seymour (mathematician) British mathematician

Paul D. Seymour is the Albert Baldwin Dod Professor of Mathematics at Princeton University. His research interest is in discrete mathematics, especially graph theory. He was responsible for progress on regular matroids and totally unimodular matrices, the four colour theorem, linkless embeddings, graph minors and structure, the perfect graph conjecture, the Hadwiger conjecture, and claw-free graphs. Many of his recent papers are available from his website.

In graph theory, an induced subgraph of a graph is another graph, formed from a subset of the vertices of the graph and all of the edges connecting pairs of vertices in that subset.

Hadwiger conjecture (graph theory)

In graph theory, the Hadwiger conjecture states that if G is loopless and has no minor then its chromatic number satisfies . It is known to be true for . The conjecture is a generalization of the four-color theorem and is considered to be one of the most important and challenging open problems in the field.

Hadwiger number

In graph theory, the Hadwiger number of an undirected graph G is the size of the largest complete graph that can be obtained by contracting edges of G. Equivalently, the Hadwiger number h(G) is the largest number k for which the complete graph Kk is a minor of G, a smaller graph obtained from G by edge contractions and vertex and edge deletions. The Hadwiger number is also known as the contraction clique number of G or the homomorphism degree of G. It is named after Hugo Hadwiger, who introduced it in 1943 in conjunction with the Hadwiger conjecture, which states that the Hadwiger number is always at least as large as the chromatic number of G.

Colin de Verdière's invariant is a graph parameter for any graph G, introduced by Yves Colin de Verdière in 1990. It was motivated by the study of the maximum multiplicity of the second eigenvalue of certain Schrödinger operators.

In graph theory, a branch of mathematics, many important families of graphs can be described by a finite set of individual graphs that do not belong to the family and further exclude all graphs from the family which contain any of these forbidden graphs as (induced) subgraph or minor. A prototypical example of this phenomenon is Kuratowski's theorem, which states that a graph is planar if and only if it does not contain either of two forbidden graphs, the complete graph K5 and the complete bipartite graph K3,3. For Kuratowski's theorem, the notion of containment is that of graph homeomorphism, in which a subdivision of one graph appears as a subgraph of the other. Thus, every graph either has a planar drawing or it has a subdivision of one of these two graphs as a subgraph.

Maria Chudnovsky Mathematician and engineer

Maria Chudnovsky is an Israeli-American mathematician working on graph theory and combinatorial optimization. She is a 2012 MacArthur Fellow.

Combinatorica is an international journal of mathematics, publishing papers in the fields of combinatorics and computer science. It started in 1981, with László Babai and László Lovász as the editors-in-chief with Paul Erdős as honorary editor-in-chief. The current editors-in-chief are László Babai, László Lovász, and Alexander Schrijver. The advisory board consists of Ronald Graham, András Hajnal, Gyula O. H. Katona, Miklós Simonovits, and Vera Sós. It is published by the János Bolyai Mathematical Society and Springer Verlag.

Jeff Kahn American mathematician

Jeffry Ned Kahn is a professor of mathematics at Rutgers University notable for his work in combinatorics. Kahn received his Ph.D. from The Ohio State University in 1979 after completing his dissertation under his advisor Dijen K. Ray-Chaudhuri.

Apex graph

In graph theory, a branch of mathematics, an apex graph is a graph that can be made planar by the removal of a single vertex. The deleted vertex is called an apex of the graph. It is an apex, not the apex because an apex graph may have more than one apex; for example, in the minimal nonplanar graphs K5 or K3,3, every vertex is an apex. The apex graphs include graphs that are themselves planar, in which case again every vertex is an apex. The null graph is also counted as an apex graph even though it has no vertex to remove.

Zdeněk Dvořák is a Czech mathematician specializing in graph theory.

References

  1. Cremation Society of Georgia: Robin Thomas
  2. 1 2 Fortnow, Lance (March 28, 2020). "Robin Thomas". Computational Complexity.
  3. Robin Thomas at the Mathematics Genealogy Project.
  4. Author biography from Berg, Deborah E.; Norine, Serguei; Su, Francis Edward; Thomas, Robin; Wollan, Paul. "Voting in agreeable societies". arXiv: 0811.3245 ..
  5. Robin Thomas Earns Distinction, Named Regents' Professor, Georgia Tech College of Computing, June 24, 2010.
  6. Robin Thomas tribute, Georgia Tech Mathematics, April 7, 2020.
  7. Fulkerson Prize: Official site with award details.
  8. Robertson, Neil; Seymour, Paul; Thomas, Robin (1993), "Hadwiger's conjecture for K6-free graphs", Combinatorica , 13 (3): 279–361, doi:10.1007/BF01202354 .
  9. Chudnovsky, Maria; Robertson, Neil; Seymour, Paul; Thomas, Robin (2006), "The strong perfect graph theorem", Annals of Mathematics , 164 (1): 51–229, arXiv: math/0212070 , doi:10.4007/annals.2006.164.51 .
  10. Karel Janeček Foundation 2011 Neuron Prize winners (in Czech) Archived 2012-12-23 at the Wayback Machine
  11. List of Fellows of the American Mathematical Society, retrieved 2013-08-27.
  12. "SIAM Announces Class of 2018 Fellows", SIAM News, March 29, 2018