Asaf Ferber

School of Physical Sciences

Publications

All of my publications can be found in the Arxiv. 

 

Selected publications:

  1. Every graph contains a linearly sized induced subgraph with all degrees odd, joint with Michael Krivelevich, submitted.
  2. Lower bounds for multicolor Ramsey numbers, joint with David Conlon, Advances in Mathematics, to appear.
  3. Singularity of random symmetric matrices — a combinatorial approach to improved bounds, joint with Vishesh Jain, Forum of Mathematics, Sigma, accepted for publication.
  4. Counting Hamilton decomposition in oriented graphs, joint with Eoin Long and Benny Sudakov, International Mathematics Research Notices.
  5. Optimal Threshold for a Random Graph to be 2-Universal, joint with Gal Kronenberg and Kyle Luh, Transaction of the American mathematical Society, to appear.
  6. Resilience for the Littlewood-Offord, joint with Afonso S. Bandeira and Matthew Kwan, Advances in Mathematics, 319 (2017), 292-312.
  7. 1-factorizations of pseudorandom graphs, joint with Vishesh Jain, FOCS ‘18.
  8. On the counting problem in inverse Littlewood-Offord theory, joint with Vishesh Jain, Kyle Luh and Wojtek Samotij, Journal of the London Mathematical Society.

 

All publications (by subject):

 

Random matrices and random sums:

  1. Sparse recovery properties of discrete random matrices, joint with Ashwin Sah, Mehtaab Sawhney, and Yizhe Zhu, submitted.
  2. Singularity of the k-core of a random graph, joint with Matthew Kwan, Ashwin Sah, and Mehtaab Sawhney, submitted.
  3. Random symmetric matrices: rank distribution and irreducibility of the characteristic polynomial, joint with Vishesh Jain,  Ashwin Sah, and Mehtaab Sawhney, submitted.
  4. Singularity of random symmetric matrices – simple proof , Comptes Rendus – Série Mathématique, to appear.
  5. Singularity of sparse random matrices — simple proofs, joint with Matthew Kwan and Lisa Sauermann, CPC, to appear.
  6. Singularity of random symmetric matrices — a combinatorial approach to improved bounds, joint with Vishesh Jain, Forum of Mathematics, Sigma, to appear.
  7. On the counting problem in inverse Littlewood-Offord theory, joint with Vishesh Jain, Kyle Luh and Wojtek Samotij, Journal of the London Mathematical Society.
  8. Resilience for the Littlewood-Offord problem, joint with Afonso S. Bandeira and Matthew Kwan, Advances in Mathematics, 319 (2017), 292-312.
  9. On the number of Hadamard matrices via anti-concentration, joint with Vishesh Jain and Yufei Zhao, submitted.
  10. Random Matrices: Law of Iterated Logarithm, joint with Daniel Montealegre and Van Vu, submitted.
  11. Resilience of the Rank of Random Matrices, joint with Kyle Luh  and Gweneth McKinley, CPC, to appear.

Random graphs:

  1. Dirac type Problem of Existence of Rainbow matchings and Rainbow Hamilton cycles in Random Graphs, joint with Jie Han and Dingjia Mao, submitted.
  2. On subgraphs with degrees of prescribed residues in the random graph, joint with Liam Hardiman and Michael Krivelevich, submitted.
  3. Friendly bisections of random graphs, joint with Matthew Kwan, Bhargav Narayanan,
  4. Ashwin Sah, and Mehtaab Sawhney, submitted.
  5. Dirac-type theorems in random hypergraphs, joint with Matthew Kwan, submitted.
  6. Co-degrees resilience for perfect matchings in random hypergraphs, joint with Lior Hirschfeld, Electronice Journal of Combinatorics.
  7. Optimal Threshold for a Random Graph to be 2-Universal, joint with Gal Kronenberg and Kyle Luh, Transactions of the American mathematical Society 372.6 (2019): 4239-4262.
  8. Counting Hamilton cycles in sparse random directed graphs, joint with Matthew Kwan and Benny Sudakov, Random Structures and Algorithms, to appear.
  9. Spanning universality in random graphs, joint with Rajko Nenadov, to appear in Random Structures and Algorithms.
  10. Packing spanning trees in random graphs, joint with Wojtek Samotij, to appear in Journal of the London Mathematical Society.
  11. Packing and Counting arbitrary Hamilton cycles in random directed graphs, joint with Eoin Long, Random Structures and Algorithms.
  12. Law of Iterated Logarithm for random graphs, joint with Daniel Montealegre and Van Vu, Random Structures and Algorithms.
  13. Packing perfect matchings in random hypergraphs, joint with Van Vu, Random Structures and Algorithms, 52 (3).
  14. Packing loose Hamilton cycles in random hypergraphs, joint with Kyle Luh, Daniel Montealegre and Oanh Nguyen, Combinatorics, Probability and Computing, 26 (6), 839-849.
  15. Embedding large graphs into a random graph, joint with Kyle Luh and Oanh Nguyen, Bulletin of the London Mathematical Society,  49 (5), 784-797
  16. Packing, Counting and Covering Hamilton cycles in random directed graphs, joint with Gal Kronenberg and Eoin Long, Israel Journal of Mathematics,  220 (1) (2017), 57-87
  17. Finding paths in sparse random graphs requires many queries, joint with Michael Krivelevich, Benny Sudakov and Pedro Vieira, Random Structures and Algorithms 50 (2017), 71-85.
  18. Strong games played on random graphs, joint with Pascal Pfister,
    The Electronic Journal of Combinatorics, Volume 24, Issue 1, 2017.
  19. Almost-spanning universality in random graphs, joint with David Conlon, Rajko Nenadov and Nemanja Skoric, Random Structures and Algorithms, 50 (3), 380-393.
  20. Finding Hamilton cycles in random graphs with few queries, joint with Michael Krivelevich, Benny Sudakov and Pedro Vieira, Random Structures and Algorithms 49 (2016), 535-668.
  21. Rainbow Hamilton cycles in random graphs and hypergraphs, joint with Michael Krivelevich, Recent trends in combinatorics, IMA Volumes in Mathematics and its applications, A. Beveridge, J. R. Griggs, L. Hogben, G. Musiker and P. Tetali, Eds., Springer 2016, 167-189.
  22. Universality of random graphs and rainbow embedding, joint with Rajko Nenadov and Ueli Peter, Random Structures and Algorithms 48 (2016), 546-564.
  23. Robust hamiltonicity of random directed graphs, joint with Rajko Nenadov, Andreas Noever, Ueli Peter, Nemanja Skoric, Journal of Combinatorial Theory Series B, also appeared at SODA’15.
  24. Closing gaps in problems related to Hamilton cycles in random graphs and hypergraphs, Electronic Journal of Combinatorics, Vol. 21, Issue 2 (2015), P1.61.
  25. Long Monotone Trails in Random Edge-Labellings of Random Graphs, joint with Omer Angel, Benny Sudakov, and Vincent Tassion,
    Combinatorics, Probability and Computing 29 (1) (2020), 22–30.

Classical graph/hypergraph theory:

  1. Number of 1-factorizations of regular high degree graphs, joint with Vishesh Jain and Benny Sudakov, Combinatorica, to appear.
  2. Towards the linear arboricity conjecture, joint with Jacob Fox and Vishesh Jain, JCTB, to appear.
  3. 1-factorizations of pseudorandom graphs, joint with Vishesh Jain, to appear in FOCS ’18.
  4. Supersaturated sparse graphs and hypergraphs, joint with Gweneth McKinley and Wojtek Samotij, International Mathematics Research Notices.
  5. Counting Hamilton decomposition in oriented graphs, joint with Eoin Long and Benny Sudakov, International Mathematics Research Notices.
  6. Packing bounded-degree spanning graphs from separable families, joint with Choongbum Lee and Frank Mousset, Israel Journal of Mathematics,  219 (2), (2017), 959-982.
  7. Counting and packing Hamilton cycles in dense graphs and oriented graphs, joint with Michael Krivelevich and Benny Sudakov, Journal of Combinatorial Theory Series B 122 (2017), 196-220.
  8. Counting and packing Hamilton l-cycles in dense hypergraphs, joint with Michael Krivelevich and Benny Sudakov, Journal of Combinatorics, 7 (2016), 135-157.
  9. On a conjecture of Thomassen, joint with Michelle Delcourt, Electronic Journal of Combinatorics, Volume 22, Issue 3.
  10. The probability of selecting $k$ edge-disjoint Hamilton cycles in the complete graph, joint with Kaarel Haenni and Vishesh Jain, submitted.
  11. Every graph contains a linearly sized induced subgraph with all degrees odd, joint with Michael Krivelevich, submitted.
  12. Lower bounds for multicolor Ramsey numbers, joint with David Conlon, Advances in mathematics, to appear.
  13. A quantitative Lovász criterion for Property B, joint with Asaf Shapira, CPC, to appear.

 

Coding theory

  1. List-decodability with large radius for Reed–Solomon codes, joint with Matthew Kwan and Lisa Sauermann, submitted.

Combinatorial designs:

  1. Almost all Steiner triple systems are almost resolvable, joint with Matthew Kwan, submitted.
  2. A construction of almost Steiner systems, joint with Rani Hod, Michael Krivelevich and Benny Sudakov, Journal of Combinatorial Designs (2014), Volume 22 (11), 488-494.

 

Positional games:

  1. Random turn games, joint with Michael Krivelevich and Gal Kronenberg, to appear in the Electronic Journal of Combinatorics.
  2. Building spanning trees quickly in Maker-Breaker games, joint with Dennis Clemens, Roman Glebov, Dan Hefetz and Anita Liebenau, SIDMA, 29 (3) (2015) , 1683-1705.
  3. Generating random graphs in biased Maker-Breaker games, joint with Michael Krivelevich and Humberto Naves, Random Structures and Algorithms, 47 (2015), 615-634.
  4. Biased Maker-Breaker games played on random boards, joint with Roman Glebov, Michael Krivelevich and Alon Naor, Random Structures and Algorithms, 46 (2015), 651-676.
  5. Weak and strong k-connectivity games, joint with Dan Hefetz, European Journal of Combinatorics (2014), pp. 169-183.
  6. Avoider-Enforcer games played on edge disjoint hypergraphs, joint with Michael Krivelevich and Alon Naor, Discrete Mathematics, 313 (2013), pp. 2932-2941.
  7. The biased odd cycle game, joint with Roman Glebov, Michael Krivelevich, Hong Liu, Cory Palmer, Tomas Valla and Mate Vizer Electronic Journal of Combinatorics Vol. 20, Issue 2 (2013), publ. P9.
  8. Fast embedding of spanning trees in biased Maker-Breaker game , joint with Dan Hefetz and Michael Krivelevich, European Journal of Combinatorics 33 (2012), 1086-1099.
  9. Fast strategies in Maker-Breaker games played on random boards , joint with Dennis Clemens, Michael Krivelevich and Anita Liebenau, Combinatorics, Probability and Computing  21 (2012), 897-915.
  10. Hitting time results for Maker-Breaker games , joint with Sonny Ben-Shimon, Dan Hefetz and Michael Krivelevich, Proceedings of the 22nd Symposium on Discrete Algorithms (SODA’11), 900-912. Random Structures and Algorithms 41 (2012), 23-46.
  11. Winning strong games through fast strategies for weak games , joint with Dan Hefetz, The Electronic Journal of Combinatorics, 18(1) 2011, P144.

Set theory:

  1. On almost precipitous ideals , joint with Moti Gitik, Archive for Mathematical Logic: Volume 49, Issue 3 (2010), Page 301.

 

Thesis:

  1. My Master’s thesis.
  2. My PhD thesis.