Lecture 8: Expanders and Applications
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چکیده
Now, it is easy to see from the definition that a complete graph is definitely an edge expander as per the above definition. For our applications, we will be mostly interested in expander graphs which have a much smaller number of edges. For example, we would be interested in d-regular graphs which are expanders with parameters d = O(1) and α = θ(1). Clearly, α cannot exceed d. The existence of such graphs is guaranteed by the following theorem which we will come back and prove at a later point in time.
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