Abstract
Each traceable graph must be a block-chain; however, a block-chain is not necessarily traceable in general. Whether a given graph is a block-chain or not can be easily verified by a polynomial algorithm. It occurs to us that forbidden subgraph conditions for a block-chain are traceable. In this article, we characterize all pairs of disconnected forbidden subgraphs for the traceability of block-chains, so as to completely solve pairs of forbidden subgraphs for the traceability of block-chains (including disconnected and connected).
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