deletions | additions       diff --git a/Monotonicity_TSP_See_ref_fig__.md b/Monotonicity_TSP_See_ref_fig__.md  index c6f8c5f..d1f209b 100644  --- a/Monotonicity_TSP_See_ref_fig__.md  +++ b/Monotonicity_TSP_See_ref_fig__.md 
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* Let \(c\) be \(d(p_{i+1}, p_{i-1})\).  * Let the length of the cycle of all points besides these three be defined as \(L\).  If we remove \(p\) from our pointset S, we can always join \(p_{i-1},p_{i+1}\) to make a new TS cycle. By the triangle inequality \(c \leq a + b\). Therefore \(|TSP(S')| = L+a+b \leq L + c = \geq  |TSP(S'_{/p})|\). This proof holds for all  ## MST