Abstract
Let c( G) denote the number of components in a graph G. It is shown that if G has genus γ and isk-connected with k ⩾ 3, then c( G − X) ⩽ (2/( k − 2))(| X | − 2 + 2 γ), for all X⊆ V( G) with | X | ⩾ k. Some implications of this result for planar graphs ( y = 0) and toroidal graphs ( y = 1) are considered.
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