Abstract
The genus γ( G) of a simple graph G is the minimum genus of the orientable surface on which G is embeddable. The thickness θ( G) of G is the minimum number of planar subgraphs of G whose union is G. From the definitions, it is clear that θ( G) = 1 if and only if γ( G) = 0. In this paper, we will show that θ( G) ≦ γ( G) + 1, if G has no triangle or if G is toroidal.
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