# optimization: cover of vertex of minimum weight in \$ G \$ connected with cycles of maximum length \$ 3 \$

Leave $$G = (V, E)$$ be a non-directed weight chart $$w: V rightarrow (0, infty)$$. We want to find an algorithm that finds a vertex cover (that is, a set of vertices so that each edge contains an element of that set)
$$U$$ from $$G$$ minimizing the amount $$w (U) = sum_ {u in U} w (u)$$ Dice
every single cycle in $$G$$ It has a length of at most $$3$$.

We are supposed to use the following fact: given an expansion tree $$T$$ from $$G$$, for all $$uv in E$$, the length of the road in $$T$$ since $$u$$ to $$v$$ it is $$1$$ or $$2$$.

I thought about using a more sophisticated version of the well-known greedy algorithm that finds a vertex cover for a tree without weights (in each iteration, find a leaf and eliminate its father, including all his children, marking the father). However, I could not generalize the underlying principles.