Tom Bohman

About

Tom Bohman is a professor in the Department of Mathematical Sciences at Carnegie Mellon University. His research focuses on combinatorics, probability, and graph theory, with significant contributions to the study of random structures, hypergraphs, and combinatorial algorithms. His work includes investigations into the evolution of random processes, hypergraph Ramsey numbers, and the properties of independent sets in hypergraphs, among other topics. Throughout his career, Bohman has authored numerous papers on topics such as the triangle-free process, hypergraph matchings, and the behavior of random graphs. His research often involves analyzing the probabilistic properties of combinatorial structures and developing algorithms for large-scale combinatorial problems. He has collaborated with various researchers and has been involved in organizing conferences and seminars related to random structures and algorithms.

Research topics

• Computer Science
• Discrete mathematics
• Combinatorics
• Mathematics
• Physics
• Optics
• Mathematical analysis

Selected publications

• Random triangle removal

  Advances in Mathematics · 2015-05-15 · 43 citations

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• A note on the random greedy independent set algorithm

  Random Structures and Algorithms · 2016-08-03 · 24 citations

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  Let r be a fixed constant and let be an r ‐uniform, D ‐regular hypergraph on N vertices. Assume further that for some . Consider the random greedy algorithm for forming an independent set in . An independent set is chosen at random by iteratively choosing vertices at random to be in the independent set. At each step we chose a vertex uniformly at random from the collection of vertices that could be added to the independent set (i.e. the collection of vertices v with the property that v is not in…

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• A natural barrier in random greedy hypergraph matching

  Combinatorics Probability Computing · 2019-06-27 · 19 citations

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  Abstract Let r ⩾ 2 be a fixed constant and let $ {\cal H} $ be an r -uniform, D -regular hypergraph on N vertices. Assume further that D → ∞ as N → ∞ and that degrees of pairs of vertices in $ {\cal H} $ are at most L where L = D/ ( log N ) ω (1) . We consider the random greedy algorithm for forming a matching in $ {\cal H} $ . We choose a matching at random by iteratively choosing edges uniformly at random to be in the matching and deleting all edges that share at least one vertex with a chosen…

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• More on the Bipartite Decomposition of Random Graphs

  Journal of Graph Theory · 2016-02-22 · 8 citations

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  For a graph , let denote the minimum number of pairwise edge disjoint complete bipartite subgraphs of G so that each edge of G belongs to exactly one of them. It is easy to see that for every graph G, , where is the maximum size of an independent set of G. Erdős conjectured in the 80s that for almost every graph G equality holds, that is that for the random graph , with high probability, that is with probability that tends to 1 as n tends to infinity. The first author showed that this is slightl…

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• The independent neighborhoods process

  Israel Journal of Mathematics · 2016-07-01 · 8 citations

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Recent grants

• Probabilistic and Extremal Combinatorics

  NSF · $270k · 2010–2013

• Probabilistic and Extremal Combinatorics

  NSF · $138k · 2007–2010

• Extremal and Probabilistic Combinatorics via Regularity and Graph Limits

  NSF · $247k · 2011–2015

Frequent coauthors

• Alan Frieze

  77 shared

• Miklós Ruszinkó

  Alfréd Rényi Institute of Mathematics

  40 shared

• Ryan R. Martin

  32 shared

• Colin Cooper

  30 shared

• Dhruv Mubayi

  13 shared

• Oleg Pikhurko

  University of Warwick

  12 shared

• Ron Holzman

  11 shared

• Eyal Lubetzky

  New York University

  8 shared

Education

• Ph.D., Mathematical Sciences

  Rutgers University

Similar researchers at Carnegie Mellon University

• Michael Youngh-57
• David Kinderlehrerh-45