Research

My research lies in combinatorics, discrete geometry, and combinatorial topology. I am mostly interested in the following areas:

  • Matching theory in graphs and hypergraphs (including geometrical hypergraphs)
  • Fair division
  • Topological methods in combinatorics.
  • Recently: Ramsey-type questions on graph edge-coloring 

And here are my publications:

  1. Tara Abrishami, Eli Berger, Maria Chudnovsky, and Shira Zerbib, Graphs with no even holes and no sector wheels are the union of two chordal graphs. Submitted. 
  2. Enrique Gomez-Leos, Emily Heath, Alex Parker, Coy Schwieder, and Shira Zerbib, New bounds on $f(n,5,8)$. Submitted. 
  3. Patrick Bennett, Emily Heath, and Shira Zerbib, Edge-coloring a graph $G$ so that every copy of a graph $H$ has an odd color class. Submitted. 
  4. Shira Zerbib, Bounds on  piercing and line-piercing numbers in families of convex sets in the plane. Submitted. 
  5. Mohsen Aliabadi and Shira Zerbib, Matchings in matroids over abelian groups. Submitted.
  6. Ron Aharoni, Eli Berger, Maria Chudnovsky and Shira Zerbib. Non-uniform degrees and rainbow versions of the Caccetta-H\"aggkvist conjecture. Submitted.
  7. Daniel McGinnis and Shira Zerbib, A sparse colorful polytopal KKM theorem. To appear in Discrete & Computational Geometry.
  8. Daniel McGinnis and Shira Zerbib, Line transversals in families of connected sets the plane. Line transversals in families of connected sets in the plane, Siam J. Discrete Math 36 (2022), no. 4, 2916–2919.
  9. Abdul Basit, Daniel McGinnis, Henry Simmons, Matt Sinnwell, and Shira Zerbib. Improved bounds on a generalization of Tuza's conjecture. Electronic Journal of Combinatorics, Volume 29, Issue 4 (2022).
  10. Bernard Lidicky, Tomas Masarik, and Kyle Murphy, and Shira Zerbib, On Weak Flexibility in Planar Graphs. Graph and Combinatorics, Volume 38, 180 (2022) .
  11. Ron Aharoni, Eli Berger, Maria Chudnovsky and Shira Zerbib, Rainbow paths and large rainbow matchings. Electronic Journal of Combinatorics Volume 29, Issue 1 (2022).
  12. Ron Aharoni, Eli Berger, Joe Briggs, Erel Segal-Halevi, and Shira Zerbib, Fractionally balanced hypergraphs and rainbow KKM theorems. To appear in Combinatorica. 
  13. Eli Berger, Krzysztof Choromanski, Maria Chudnovski, and Shira Zerbib, Tournaments and the Strong Erdos-Hajnal Property. European Journal of Combinatorics 100 (2022).
  14. Kathryn Nyman, Francis E. Su and Shira Zerbib,  Fair division with multiple pieces. Discrete Applied Mathematics, 283 (2020), 115--122.
  15. Ron Aharoni and Shira Zerbib, A generalization of Tuza's conjecture. Journal of Graph Theory, 94 (2020), no. 3, 445--462.
  16. Patrick Bennett, Andrzej Dudek and Shira Zerbib, Large triangle packings and Tuza's conjecture in sparse random graphs. Combinatorics, Probability and Computing, 29 (2020), no. 5, 757--779.
  17. Deborah Oliveros, Christopher O'Neill and Shira Zerbib, The geometry and combinatorics of discrete line segment hypergraphs.  Discrete Mathematics, 343 (2020), no. 6.
  18. Frederic Meunier and Shira Zerbib, Envy-free cake division without assuming the players prefer non-empty pieces. Israel Journal of Mathematics, 234 (2019), no. 2, 907--925.
  19. Shira Zerbib, An improved bound in Vizing's conjecture. Graphs and Combinatorics, 35 (2019), no. 6, 1401--1404.
  20. Francis E. Su and Shira Zerbib,  Piercing Numbers in Approval Voting. Mathematical Social Sciences 101 (2019), 65–71.
  21. Shiliang Gao and Shira Zerbib,  The (2,2) and (4,3) properties in families of fat sets in the plane. SIAM Journal of Discrete Math,  33 (2019), no. 3, 1326–1337. (This paper was written as part of an REU project I mentored during summer 2017. Shiliang won the George Piranian Excellence in Mathematical Writing Award for it.)
  22. Florian Frick and Shira Zerbib, Colorful coverings of polytopes and piercing numbers of colorful d-intervals. Combinatorica 39 (2019), no. 3, 627–637.  
  23. Roy Meshulam and Shira Zerbib, On Lusztig-Dupont homology of flag complexes. Journal of Algebra, 531 (2019), 83–101. 
  24. Shira Zerbib, The (p,q) property in families of d-intervals and d-trees. Discrete Mathematics 342(4) (2019) 1089-1097. 
  25. Maria Chudnovsky, Sophie Spirkl and Shira Zerbib, Piercing axis-parallel boxes. Electronic Journal of Combinatorics, Volume 25, Issue 1 (2018). 
  26. Ron Aharoni, Ron Holzman and Shira Zerbib, Edge-covers in d-interval hypergraphs. Discrete & Computational Geometry 58(3) (2017) 650-662. 
  27. Ron Aharoni, Tomas Kaiser and Shira Zerbib, Fractional covers and matchings in families of weighted d-intervals. Combinatorica 37(4) (2016) 555-572. 
  28. Gabriel Nivasch, Janos Pach, Rom Pinchasi and Shira Zerbib, The number of distinct distances from a vertex of a convex polygon. Journal of Computational Geometry 4(1) (2013) 1-12. 
  29. Shira Zerbib, On the zone complexity of a vertex. SIAM Journal Discrete Math. 25(2) (2011) 719-730.
     

My papers on arXiv.

Here are (loosely edited) lecture notes on KKM-type theorems and their applications in combinatorics and discrete geometry.