Phase transitions in random combinatorial structures

Mihyun Kang

Team:

Subproject Leader: Mihyun Kang

PostDoc: Ronen Wdowinski, Mike Liu

Former Member: Michail Sarantis (PostDoc, 01.09.2024 - 31.01.2026)

Results:

• Bootstrap percolation on the high dimensional Hamming graph.
  Mihyun Kang, Michael Missethan, Dominik Schmid
  SIAM Journal on Discrete Mathematics (2025), Vol. 39, Nr. 4.
  DOI: 10.1137.24M1670937 (associated to Project 5)
• Universal behaviour of majority bootstrap percolation on high-dimensional geometric graphs.
  Mauricio Collares, Joshua Erde, Anna Geisler, Mihyun Kang
  arXiv:2406.17486 (associated to Project 5) 
• Large matchings and nearly spanning, nearly regular subgraphs of random subgraphs.
  Sahar Diskin, Joshua Erde, Mihyun Kang, and Michael Krivelevich 
  Electron J. Comb. (2026), Vol. 33, No. 1, P1.37.
  DOI: 10.37236/14036 (associated to Project 5)
• Universality of the matching number in percolated regular graphs
  Sahar Diskin, Mihyun Kang, and Lyuben Lichev
  arXiv:2503.11242 (associated to Project 5)
• Counting independent sets in expanding bipartite regular graphs
  Mauricio Collares, Joshua Erde, Anna Geisler, and Mihyun Kang
  arXiv:2503.22255 (associated to Project 5)
• Nearly spanning cycle in the percolated hypercube
  Michael Anastos, Sahar Diskin, Joshua Erde, Mihyun Kang, Michael Krivelevich, and Lyuben Lichev
  arXiv:2505.04436 (associated to Project 5)
• Cycle lengths in the percolated hypercube
  Michael Anastos, Sahar Diskin, Joshua Erde, Mihyun Kang,  Michael Krivelevich and Lyuben Lichev
  arXiv:2506.16858 (associated to Project 5)
• Hall's theorem for reconfigurations and higher dimensional topological connectedness
  Ronen Wdowinski
  arXiv:2511.04863 (associated to Project 5)
• Fragile minor-monotone parameters under a random edge perturbation 
  Dong Yeap Kang, Mihyun Kang, Jaehoon Kim, and Sang-il Oum 
  European Journal of Combinatorics (2026), Vol. 133, 104305 
  DOI: 10.1016/j.ejc.2025.104305 (associated to Project 5)
• Bounded degree graphs and hypergraphs with no full rainbow matchings 
  Ronen Wdowinski 
  European Journal of Combinatorics (2026), Vol. 133, 104316 
  DOI: 10.1016/j.ejc.2025.104316 (associated to Project 5)
• On the number of antichains in {0,1,2}^n
  Matthew Jenssen, Jinyoung Park, and Michail Sarantis
  arXiv:2601.07650 (associated to Project 5)
• Counting independent sets in percolated graphs via the Ising model
  Anna Geisler, Mihyun Kang, Michail Sarantis, and Ronen Wdowinski 
  Random Structures Algorithms (2026), 68, no. 1: e70044. 
  DOI: 10.1002/rsa.70044 (associated to Project 5)
• Sampling from the antiferromagnetic Ising model on bipartite, regular expander graphs
  Anna Geisler, Mihyun Kang, Michail Sarantis, Ronen Wdowinski
  arXiv:2603.02101 (associated to Project 5)
• Tight constructions for reconfigurations of independent transversals
  Ronen Wdowinski 
  arXiv:2604.21576 (associated to Project 5)
• Uniqueness and locality of the ground state of the disordered Monomer-Dimer models on independently weighted Unimodular Bienaymé-Galton-Watson trees
  Mihyun Kang and Mike Liu
  arXiv:2603.19003 (associated to Project 5)
• Counting subgraphs in bounded-size Achlioptas processes
  Mihyun Kang and Oliver Riordan
  arXiv: 2605.09466 (associated to Project 5)     
• Percolation through Isoperimetry
  Sahar Diskin, Joshua Erde, Mihyun Kang, and Michael Krivelevich,
  Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 2026, Vol. 62, No. 2, 900-918,
  DOI: 10.1214/24-AIHP1533 (associated to Project 5)