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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...

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