Consider the simple random graph constructed as follows. There are n > 2 vertices V1, V2, . . . , Vn that comprise the vertex set V. Each pair of vertices is adjacent with probability p, where p E [0, 1], independently of other pairs of vertices. Let G' be a fixed graph such that • The vertex set of G' is V' = {v1, v2, ... , Vm}, with 2 < m < n. • It has e > 1 edges. What is the probability that G' is a subgraph of G?

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Consider the simple random graph constructed as follows. There are n > 2 vertices
V1, V2, . . . , Vn that comprise the vertex set V. Each pair of vertices is adjacent with
probability p, where p E [0, 1], independently of other pairs of vertices.
Let G' be a fixed graph such that
• The vertex set of G' is V' = {v1, v2, .
Vm}, with 2 < m< n.
...
• It has e > 1 edges.
What is the probability that G' is a subgraph of G?
Transcribed Image Text:Consider the simple random graph constructed as follows. There are n > 2 vertices V1, V2, . . . , Vn that comprise the vertex set V. Each pair of vertices is adjacent with probability p, where p E [0, 1], independently of other pairs of vertices. Let G' be a fixed graph such that • The vertex set of G' is V' = {v1, v2, . Vm}, with 2 < m< n. ... • It has e > 1 edges. What is the probability that G' is a subgraph of G?
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