It is shown that [(G)/3] is the tight lower bound on the maximum genus M(G) of 2-edge-connected simplicial graphs, where (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 M(G) = [(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.
