 Solution

ID: past-exam-of-the-probability-statistics-and-options-i-course-of-the-university-of-oxford/2011/r/1/b/solution

K_{2, 3}

is connected and has five vertices and six edges. It is a planar graph, as in the right drawing above. Euler formula for a connected planar graph therefore gives

f = 2 - v + e = 2 - 5 + 6 = 3.

This includes the unbounded exterior face.

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