The lower bounds on the maximum genus of loopless graphs are obtained according to the connectivity of these graphs. This not only answers a question of Chen, Archdeacon and Gross, but also generalizes the previous kn...The lower bounds on the maximum genus of loopless graphs are obtained according to the connectivity of these graphs. This not only answers a question of Chen, Archdeacon and Gross, but also generalizes the previous known results. Thus, a picture of the lower bounds on the maximum genus of loopless multigraphs is presented.展开更多
It is proved that every 3 connected loopless multigraph has maximum genus at least one third of its cycle rank plus one if its cycle rank is not less than ten, and if its cycle rank is less than ten,it is upper emb...It is proved that every 3 connected loopless multigraph has maximum genus at least one third of its cycle rank plus one if its cycle rank is not less than ten, and if its cycle rank is less than ten,it is upper embeddable.This lower bound is tight.There are infinitely many 3 connected loopless multigraphs attaining this bound.展开更多
Abstract In this paper, the relationship between non separating independent number and the maximum genus of a 3 regular simplicial graph is presented. A lower bound on the maximum genus of a 3 regular graph involving ...Abstract In this paper, the relationship between non separating independent number and the maximum genus of a 3 regular simplicial graph is presented. A lower bound on the maximum genus of a 3 regular graph involving girth is provided. The lower bound is tight, it improves a bound of Huang and Liu.展开更多
文摘The lower bounds on the maximum genus of loopless graphs are obtained according to the connectivity of these graphs. This not only answers a question of Chen, Archdeacon and Gross, but also generalizes the previous known results. Thus, a picture of the lower bounds on the maximum genus of loopless multigraphs is presented.
文摘It is proved that every 3 connected loopless multigraph has maximum genus at least one third of its cycle rank plus one if its cycle rank is not less than ten, and if its cycle rank is less than ten,it is upper embeddable.This lower bound is tight.There are infinitely many 3 connected loopless multigraphs attaining this bound.
文摘Abstract In this paper, the relationship between non separating independent number and the maximum genus of a 3 regular simplicial graph is presented. A lower bound on the maximum genus of a 3 regular graph involving girth is provided. The lower bound is tight, it improves a bound of Huang and Liu.
