The study of discrete mathematical structures. Consider using a more specific tag instead, such as: (combinatorics), (graph-theory), (computer-science), (probability), (elementary-set-theory), (induction), (recurrence-relations), etc.

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Find the finite sequence that minimizes the value of $T_5(P)$

Given a finite sequence $P(a_1,b_1),(a_2,b_2),...,(a_n,b_n)$, define $T_1(P):=a_1+b_1$, $\forall 2\leq k\leq n$, $T_k(P)=b_k+\max\{T_{k-1}(P),a_1+a_2+...+a_k\}$. Let $m=\min\{a,b,c,d\}$. ...
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The graph has an Euler tour iff in-degree($v$)=out-degree($v$)

I am looking at the proof that $G$ has an Euler tour iff in-degree($v$)=out-degree($v$), that I found at this site: www.cs.duke.edu/courses/fall09/cps230/hws/hw3/headsol.pdf (Problem 2) A simple ...