Complexity of existance a weighted cycle

Question

Assume weighted Graph G, vertices and edges are weighted, and given constant k, what is the complexity of following decision problem A?

1-A: Dose G contane cycle with total weight K?
2- what is the complexity of A if G is a plannar graph?

Any idea or pointing to papers or book is also welcome!

Answer 1

它是NP完全的，因为您可以使用单位权重和k = n从平面哈密​​顿循环中减少。