哈密尔顿平面图最小平衡二部划分的上界

设$G（V，E）$是一个图，$V_{1}，V_{2}$是$V$的一个二部划分，用$e（V_{1}，V_{2}）$表示一条边的两个端点在不同划分里边的总数目，当$||V_{1}|-|V_{2}||\leq 1$时，称$V_{1}，V_{2}$是$V$的一个平衡二部划分。最小平衡二部划分是指寻找$G（V，E）$的一个平衡二部划分使得$e（V_{1}，V_{2}）$最小。对于哈密尔顿平面图$G（V，E）$，研究了当Perfect-内部三角形最大边函数值与最小边函数值之差为$d$时，$e（V_{1}，V_{2}）$最小值的上界与$d$之间的关系。

Upper bounds on minimum balanced bipartition of Hamilton plane graphs

A balanced bipartition of a graph $G(V,E)$ is a bipartition $V_{1}$ and $V_{2}$ of V(G) such that $||V_{1}|-|V_{2}||\leq 1$. The minimum balanced bipartition problem asks for a balanced bipartition minimizing $e(V_{1},V_{2})$, where $e(V_{1},V_{2})$ is the number of edges joining $V_{1}$ and $V_{2}$. In this paper, for Hamilton plane graphs, we study the relation between upper bounds on the minimum of $e(V_{1},V_{2})$ and $d$, which is the difference between the maximum edge function value and the minimum edge function value of Perfect-inner triangle.