Abstract We derive a sharp lower bound for the scalar curvature of non-flat and non-compact expanding gradient Ricci soliton provided that is non-negative potential function proper. Upper expander with nonpositive will also be given. Furthermore, we provide sufficient condition being non-negative. Curvature estimates solitons in dimensions three four established. As an application, prove gap th...

In this paper, we consider a structural and geometric property of graphs, namely the presence large expanders. The problem finding such structures was first considered by Krivelevich [SIAM J. Disc. Math. 32 1 (2018)]. Here, show that induced subgraph is an expander can be reduced to simpler topological minor expander. Our proof constructive, which helpful in algorithmic setting.
 We also e...

We show how to compute O( √ logn)-approximations to Sparsest Cut and Balanced Separator problems in Õ(n) time, thus improving upon the recent algorithm of Arora, Rao and Vazirani (2004). Their algorithm uses semidefinite programming and required Õ(n) time. Our algorithm relies on efficiently finding expander flows in the graph and does not solve semidefinite programs. The existence of expander ...

We give a new lower bound on the expansion coefficient of an edge-vertex graph of a d-regular graph. As a consequence, we obtain an improvement on the lower bound on relative minimum distance of the expander codes constructed by Sipser and Spielman. We also derive some improved results on the vertex expansion of graphs that help us in improving the parameters of the expander codes of Alon, Bruc...

It is known that random 2-lifts of graphs give rise to expander graphs. We present a new conjectured derandomization of this construction based on certain Mealy automata. We verify that these graphs have polylogarithmic diameter, and present a class of automata for which the same is true. However, we also show that some automata in this class do not give rise to expander graphs.

Expander graphs are one of the deepest tools of theoretical computer science and discrete mathematics, popping up in all sorts of contexts since their introduction in the 1970s. Here’s a list of some of the things that expander graphs can be used to do. Don’t worry if not all the items on the list make sense: the main thing to take away is the sheer range of areas in which expanders can be appl...