Complexity of existence of m-cycle in planar graph with n nodes

G is a planar graph with n nodes.

What are the complexity of following problems?

1. A: Does G contain a m-cycle? (m开发者_开发问答-cycle is a simple cycle with m nodes, m
2. B: complexity of counting all m-cycles in G.
3. what is the complexity of A and B if G is an arbitrary given graph?

Pointing to books and papers is also useful...