A NOTE ON THE MAXIMUM GENUS OF 3-EDGE-CONNECTED NONSIMPLE GRAPHS
HuangYuanqiu · Acta Scientiarum Naturalium Universitatis Sunyatseni · 2000
Let G be a 3-edge-connected graph (possibly with multiple edges or loops), and let γM(G) and β(G) be the maximum genus and the Betti number of G, respectively. Then γM(G)≥β(G)/3 can be proved and this answers a question posed by Chen, et al. in 1996.