The Grothendieck constant of random and pseudo-random graphs

The Grothendieck constant of random and pseudo-random graphs

The Grothendieck constant of a graph G = (V,E) is the least constant K such that for every matrix A : V × V → R: max f :V→S|V |−1 ∑ {u,v}∈E A(u, v) · 〈f(u), f(v)〉 ≤ K max :V→{−1,+1} ∑ {u,v}∈E A(u, v) · (u) (v). The investigation of this parameter, introduced in [2], is motivated by the algorithmic problem of maximizing the quadratic form ∑ {u,v}∈E A(u, v) (u) (v) over all : V → {−1, 1}, which a...

Random and Pseudo-Random Walks on Graphs

Random walks on graphs have turned out to be a powerful tool in the design of algorithms and other applications. In particular, expander graphs, which are graphs on which random walks have particularly good properties, are extremely useful in complexity and other areas of computer science. In this chapter we study random walks on general regular graphs, leading to a the randomized logspace algo...

Random and Pseudo-Random Walks on Graphs

Random walks on graphs have turned out to be a powerful tool in the design of algorithms and other applications. In particular, expander graphs, which are graphs on which random walks have particularly good properties, are extremely useful in complexity and other areas of computer science. In this chapter we will study random walks on general graphs, leading to a the randomized logspace algorit...

Pseudo-random Graphs

Random graphs have proven to be one of the most important and fruitful concepts in modern Combinatorics and Theoretical Computer Science. Besides being a fascinating study subject for their own sake, they serve as essential instruments in proving an enormous number of combinatorial statements, making their role quite hard to overestimate. Their tremendous success serves as a natural motivation ...

List oloring of random and pseudo-random graphs