• Publications
  • Influence
Expander Graphs and their Applications
A major consideration we had in writing this survey was to make it accessible to mathematicians as well as to computer scientists, since expander graphs, the protagonists of our story, come up inExpand
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The Moore Bound for Irregular Graphs
TLDR
We extend the Moore bound to cover irregular graphs, yielding an affirmative answer to an old open problem. Expand
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On codes from hypergraphs
TLDR
We propose a new family of asymptotically good binary codes, generalizing previous constructions of expander codes to t-uniform hypergraphs. Expand
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Rank Bounds and Integrality Gaps for Cutting Planes Procedures
TLDR
We present a new method for proving rank lower bounds for Cutting Planes (CP) and several procedures based on Lovász and Schrijver (LS), when viewed as proof systems for unsatisfiability. Expand
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The Size of Bipartite Graphs with a Given Girth
  • S. Hoory
  • Computer Science, Mathematics
  • J. Comb. Theory, Ser. B
  • 1 November 2002
What is the maximum number of edges in a bipartite graph of girth g whose left and right sides are of size nL, nR? We generalize the known results for g = 6, 8 to an arbitrary girth.
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Linear-Time Reductions of Resolution Proofs
TLDR
We propose two methods that are linear in the size of the proof for doing so. Expand
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Universal Traversal Sequences for Expander Graphs
TLDR
Graph reachability is a key problem in the study of various logarithmic space complexity classes. Expand
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A Note on Unsatisfiable k-CNF Formulas with Few Occurrences per Variable
TLDR
The (k,s)-SAT problem is the satisfiability problem restricted to instances where each clause has exactly k literals and every variable occurs at most s times. Expand
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THE NON-BACKTRACKING SPECTRUM OF THE UNIVERSAL COVER OF A GRAPH
A non-backtracking walk on a graph, H, is a directed path of directed edges of H such that no edge is the inverse of its preceding edge. Non-backtracking walks of a given length can be counted usingExpand
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Rank bounds and integrality gaps for cutting planes procedures
TLDR
We present a new method for proving rank lower bounds for Cutting Planes and Lovasz-Schrijver proofs for several prominent CNF examples, including random kCNF formulas and the Tseitin graph formulas. Expand
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