Abstract
It is shown that ⌈ β( G)/3⌉ is the tight lower bound on the maximum genus γ M( G) of 2-edge-connected simplicial graphs, where β( G) is the cycle rank of the graph G. Also, a systematic method is developed to construct 3-vertex-connected simplicial graphs G satisfying the equality γ M( G) = ⌈ β( G)/3⌉. These two results combine with previously known results to yield a complete picture of the tight lower bounds on the maximum genus of simplicial graphs.
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