Slides

On this page, I will give some more slides and background for my papers. First, here is the list of my papers again:

Peer-Reviewed Publications:

1. Tolson Bell and Alan Frieze.
   "Solving a Random Asymmetric TSP Exactly in Quasi-Polynomial Time w.h.p" (2026).
   Random Structures and Algorithms, Vol. 68: Issue 2, Article 2.
   Arxiv: 2308.02946. 23 pages.

2. Tolson Bell and Alan Frieze.
   "Giant Rainbow Trees in Sparse Random Graphs" (2025).
   European Journal of Combinatorics, Vol. 128: 104184.
   Arxiv: 2308.14141. 9 pages.

3. Tolson Bell and Alan Frieze.
   "O(1) Insertion for Random Walk d-ary Cuckoo Hashing up to the Load Threshold" (2024).
   Foundations of Computer Science (FOCS), 2024 Proceedings: Pages 106-119.
   Invited to FOCS Special Issue of SIAM Journal on Computing (SICOMP).
   Arxiv: 2401.14394. 31 pages.

4. Tolson Bell, Alan Frieze, and Trent Marbach.
   "Rainbow Thresholds" (2024).
   SIAM Journal on Discrete Mathematics (SIDMA), Vol. 38: Issue 3, Article 18.
   Arxiv: 2104.05629. 10 pages.

5. Tolson Bell and Alan Frieze.
   "Rainbow Powers of a Hamiltonian Cycle in G(n,p)" (2024).
   Journal of Graph Theory, Vol. 105: Issue 4, Article 1.
   Arxiv: 2210.08534. 9 pages.

6. Tolson Bell.
   "The Park-Pham Theorem with Optimal Convergence Rate" (2023).
   Electronic Journal of Combinatorics, Vol. 30: Issue 2, Article 25.
   Arxiv: 2210.03691. 8 pages.

7. Tolson Bell, Jerrell Cockerham, Clayton Mizgerd, Melita Wiles, and Christian Scullard.
   "Critical Points of the Random Cluster Model with Newman-Ziff Sampling" (2022).
   Journal of Physics A, Vol. 55: Issue 4, Article 1.
   Arxiv: 2102.12716. 10 pages.

8. Tolson Bell, Suchakree Chueluecha, and Lutz Warnke.
   "Note on Sunflowers" (2021).
   Discrete Mathematics, Vol. 344: Issue 7, Article 7.
   Arxiv: 2009.09327. 3 pages.

9. Tolson Bell, David Luo, Luke Seaton, and Samuel Serra.
   "Gordian Adjacency for Positive Braid Knots" (2020).
   Rose-Hulman Undergraduate Math Journal, Vol. 21: Issue 2, Article 5.
   Arxiv: 1910.02933. 23 pages.

O(1) Insertion for Cuckoo Hashing (#3): This paper has undergone a major revision from its first (FOCS) version in order to fix an error in the earlier version. The result of the later version is stronger in that it also finishes the d=3 hashes case. However, the "tail bounds" on the number of evictions got slightly weaker in the later version.

Slides (from a probabilistic combinatorics perspective)

Presentation Video (from a CS theory perspective) (from the earlier version)

Poster (from the earlier version)

Random Cluster Model (#7) - From the 2021 Research in Industrial Projects for Students Program (RIPS)

At Institute for Pure and Applied Mathematics (IPAM) at UCLA

Sponsored by Lawrence Livermore National Lab (LLNL)

Slides

Gordian Adjacency (#9) - A project from the 2018 REU at Michigan State University

Slides