改正了文章“与直径和围长有关的最大亏格的下界(数学学报2004,47(6):1201—1204)”中的一个错误结论,并得到了如下结果:设G是直径为d(G)的简单图,若G的围长g(G)≥d(G),则 ξ(G)≤2,从而γM(G)≥1/2β(G)-1.
We correct an error in the paper "The Lower Bounds of the Maximum Genus on Graphs in Terms of Diameter and Girth" (Acta Mathematica Sinica, 2004, 47(6): 1201-1204), and obtain the following result: Let G be a simple graph with diameter d. If its girth is not less than d, then the Betti deficiency number of G, ξ(G) ≤ 2, i.e. the maximum genus of G, γM(G) ≥ 1/2β(G) - 1.