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If T is a spanning threshold subgraph of G and GX is an induced subgraph of G, then TX is a spanning threshold subgraph of GXTherefore t(G) ⩾ t(GX), in particular t (G) ≥ max (t (G) C, t (G) Q)On the other hand, if T C is a spanning threshold subgraph of GC and T Q is a spanning threshold subgraph of GQ, then the spanning subgraph of G consisting of the edges of T C ∪ T.

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