It is known (for example, see [4]) that the maximum genus of a graph is mainly determined by the Betti deficiency of the graph. In this paper, we establish a best upper bound on the Betti deficiency of a graph bounded...It is known (for example, see [4]) that the maximum genus of a graph is mainly determined by the Betti deficiency of the graph. In this paper, we establish a best upper bound on the Betti deficiency of a graph bounded by its independence number and girth, and immediately obtain a new result on the maximum genus.展开更多
It is known (for example see [2]) that the maximum genus of a graph is mainly determined by the Betti deficiency of the graph. In this paper, the authors establish an upper bound on the Betti deficiency in terms of th...It is known (for example see [2]) that the maximum genus of a graph is mainly determined by the Betti deficiency of the graph. In this paper, the authors establish an upper bound on the Betti deficiency in terms of the independence number as well as the girth of a graph, and thus use the formulation in [2] to translate this result to lower bound on the maximum genus. Meantime it is shown that both of the bounds are best possible.展开更多
基金Supported by the National Natural Scicnce Foundation of China !(19801013)
文摘It is known (for example, see [4]) that the maximum genus of a graph is mainly determined by the Betti deficiency of the graph. In this paper, we establish a best upper bound on the Betti deficiency of a graph bounded by its independence number and girth, and immediately obtain a new result on the maximum genus.
基金National Natural Science Foundation of China!(No.19801013).
文摘It is known (for example see [2]) that the maximum genus of a graph is mainly determined by the Betti deficiency of the graph. In this paper, the authors establish an upper bound on the Betti deficiency in terms of the independence number as well as the girth of a graph, and thus use the formulation in [2] to translate this result to lower bound on the maximum genus. Meantime it is shown that both of the bounds are best possible.
