A key feature of Simonovits' proof of the classic Erdős-Pósa theorem is a simple subgraph of the host graph, a frame, that determines the outcome of the theorem. We transfer this frame technique to A-paths. With it we deduce a simple proof of Gallai's theorem, although with a worse bound, and we verify the Erdős-Pósa property for long and for even A-paths. We also show that even A-paths do not have the edge-Erdős-Pósa property.

I prove that even A-cycles have the edge-Erdős-Pósa property.

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