@article{22752,
  abstract     = {In this note we outline a new and simple approach to proving central limit theorems for various ‘global’ graph parameters that have robust ‘local’ approximations, using the Efron–Stein inequality, which relies on a combinatorial analysis of the stability of these approximations under resampling an edge. As an application, we give short proofs of a central limit theorem for the order of the giant component and of the 𝑘
-core for sparse random graphs.},
  author       = {Anastos, Michael and Erde, Joshua and Kang, Mihyun and Pfenninger, Vincent},
  issn         = {1469-2120},
  journal      = {Bulletin of the London Mathematical Society},
  number       = {8},
  publisher    = {Wiley},
  title        = {{A short proof of a central limit theorem for the order of the giant component and k-core}},
  doi          = {10.1112/blms.70464},
  volume       = {58},
  year         = {2026},
}

@article{19798,
  abstract     = {In an  n×n  array filled with symbols, a transversal is a collection of entries with distinct rows, columns and symbols. In this note we show that if no symbol appears more than  βn  times, the array contains a transversal of size  (1−β/4−o(1))n . In particular, if the array is filled with  n  symbols, each appearing  n  times (an equi- n  square), we get transversals of size  (3/4−o(1))n. Moreover, our proof gives a deterministic algorithm with polynomial running time, that finds these transversals.},
  author       = {Anastos, Michael and Morris, Patrick},
  issn         = {1520-6610},
  journal      = {Journal of Combinatorial Designs},
  number       = {9},
  pages        = {338--342},
  publisher    = {Wiley},
  title        = {{A note on finding large transversals efficiently}},
  doi          = {10.1002/jcd.21990},
  volume       = {33},
  year         = {2025},
}

@inproceedings{20007,
  abstract     = {There is no known polynomial-time algorithm for graph isomorphism testing, but elementary combinatorial “refinement” algorithms seem to be very efficient in practice. Some philosophical justification for this phenomenon is provided by a classical theorem of Babai, Erdős and Selkow: an extremely simple polynomial-time combinatorial algorithm (variously known as “naïve refinement”, “naïve vertex classification”, “colour refinement” or the “1-dimensional Weisfeiler–Leman algorithm”) yields a so-called canonical labelling scheme for “almost all graphs”. More precisely, for a typical outcome of a random graph G(n,1/2), this simple combinatorial algorithm assigns labels to vertices in a way that easily permits isomorphism-testing against any other graph.},
  author       = {Anastos, Michael and Kwan, Matthew Alan and Moore, Benjamin},
  booktitle    = {Proceedings of the 57th Annual ACM Symposium on Theory of Computing},
  isbn         = {9798400715105},
  issn         = {0737-8017},
  location     = {Prague, Czechia},
  pages        = {2098--2106},
  publisher    = {Association for Computing Machinery},
  title        = {{Smoothed analysis for graph isomorphism}},
  doi          = {10.1145/3717823.3718173},
  year         = {2025},
}