Upper embeddability,edge independence number and girth

Combined with the edge-connectivity, this paper investigates the relationship between the edge independence number and upper embeddability. And we obtain the following result: Let G be a k-edge-connected graph with girth g. If α ’(G)≤((k-1)2+2) [g/2]+(1-(-1)n)/2((k-1)(k-2)+1)-1,where k =1, 2, 3, and α (G) denotes the edge independence number of G, then G is upper embeddable and the upper bound is best possible. And it has generalized the relative results.