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Expansion and random walks in SL d ( / p n ) : I

Jean Bourgain, Alex Gamburd (2008)

Journal of the European Mathematical Society

We prove that the Cayley graphs of SL d ( / p n ) are expanders with respect to the projection of any fixed elements in SL d ( ) generating a Zariski dense subgroup.

Expansion in finite simple groups of Lie type

Emmanuel Breuillard, Ben J. Green, Robert Guralnick, Terence Tao (2015)

Journal of the European Mathematical Society

We show that random Cayley graphs of finite simple (or semisimple) groups of Lie type of fixed rank are expanders. The proofs are based on the Bourgain-Gamburd method and on the main result of our companion paper [BGGT].

Expansion in S L d ( 𝒪 K / I ) , I square-free

Péter P. Varjú (2012)

Journal of the European Mathematical Society

Let S be a fixed symmetric finite subset of S L d ( 𝒪 K ) that generates a Zariski dense subgroup of S L d ( 𝒪 K ) when we consider it as an algebraic group over m a t h b b Q by restriction of scalars. We prove that the Cayley graphs of S L d ( 𝒪 K / I ) with respect to the projections of S is an expander family if I ranges over square-free ideals of 𝒪 K if d = 2 and K is an arbitrary numberfield, or if d = 3 and K = .

Exploiting the structure of conflict graphs in high level synthesis

Klaus Jansen (1994)

Commentationes Mathematicae Universitatis Carolinae

In this paper we analyze the computational complexity of a processor optimization problem. Given operations with interval times in a branching flow graph, the problem is to find an assignment of the operations to a minimum number of processors. We analyze the complexity of this assignment problem for flow graphs with a constant number of program traces and a constant number of processors.

Exponents of two-colored digraphs

Yan Ling Shao, Yubin Gao (2009)

Czechoslovak Mathematical Journal

We consider the primitive two-colored digraphs whose uncolored digraph has n + s vertices and consists of one n -cycle and one ( n - 3 ) -cycle. We give bounds on the exponents and characterizations of extremal two-colored digraphs.

Extended trees of graphs

Bohdan Zelinka (1994)

Mathematica Bohemica

An extended tree of a graph is a certain analogue of spanning tree. It is defined by means of vertex splitting. The properties of these trees are studied, mainly for complete graphs.

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