Sorting in c log n parallel steps
Combinatorica
Colorings and homomorphisms of degenerate and bounded degree graphs
Discrete Mathematics
Explicit constructions of Ramanujan complexes of type Ad
European Journal of Combinatorics - Special issue on combinatorics and representation theory
An elementary construction of constant-degree expanders
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Forbidden lifts (NP and CSP for combinatorialists)
European Journal of Combinatorics
Non-bipartite pairs of 3-connected graphs are highly Ramsey-infinite
European Journal of Combinatorics
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We give a poly-time construction for a combinatorial classic known as Sparse Incomparability Lemma, studied by Erd驴s, Lovász, Nešetřil, Rödl and others: We show that every Constraint Satisfaction Problem is poly-time equivalent to its restriction to structures with large girth. This implies that the complexity classes CSP and Monotone Monadic Strict NP introduced by Feder and Vardi are computationally equivalent. The technical novelty of the paper is a concept of expander relations and a new type of product for relational structures: a generalization of the zig-zag product, the twisted product.