摘要
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 $$ \alpha '(G) \leqslant ((k - 2)^2 + 2)\left\lfloor {\frac{g} {2}} \right\rfloor + \frac{{1 - ( - 1)^g }} {2}((k - 1)(k - 2) + 1) - 1, $$ 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.
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.
基金
supported by National Natural Science Foundation of China (Grant No.10771062)
New Century Excellent Talents in University (Grant No.NCET-07-0276)
