Consider a complete undirected graph G $=($V$,$ E$)$ in which all edge lengths

are either $1$ or $2.$ Propose a $4/3-$approximation algorithm for the Traveling

Salesman Problem on such graphs.

Hint: A $2-$matching is a subset S of edges such that every vertex has exactly

$2$ edges of S incident on it$.$ For a start, find a minimum $2-$matching in G$.$ You

may assume that a $2-$matching can be found in polynomial$-$time.

all solution given do not provide a good proof

please give me a full proof of approximation explaining exactly why its tru to the very detail and explain why we got to $4/3$ aproximation very clearly and ot jump to the conclusion

its important to explain every step and start the proof explaining every step

and the algorithm needs to be explained clearly