Maximum genus and connectivity Original Research Article

It is shown that ⌈β(G)/3⌉ is the tight lower bound on the maximum genus γM(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 γM(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.