In connected graphs of minimum degree 3 with n ≥ 18, the minimum number of longest paths (detours) is exactly 36, with related upper bounds for general k and odd counts.
West, Introduction to Graph Theory, Prentice Hall, Inc., 19 96
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The minimum number of detours in a connected graph of minimum degree three
In connected graphs of minimum degree 3 with n ≥ 18, the minimum number of longest paths (detours) is exactly 36, with related upper bounds for general k and odd counts.