Liu created joint trees, initiated in his early paper in 1979, of a graph in 2003 which provided a foundation on studying embedding genus distribution.
2003年刘提出的图的联树（1979的文章体现了这种思想）为嵌入亏格分布的研究提供了理论基础。
Intrinsically knotted and 3-linked graphs, that is, every spatial embedding of this graph contains nontrivial knot and a non-split 3-component link.
内在纽结与3-链图，即：这个图的每个空间嵌入中都包含非平凡的纽结和分支数为3的非分离链环。
This is the problem of embedding genus distribution for a graph.
这就是图的嵌入亏格分布问题。
There are two fields in topological graph theory: one is the study of the properties of graph embedding.
本文研究属第一个方面，即研究图的嵌入的最大亏格问题。
On the basis of the joint tree model, an embedding of a graph on a surface can be rep-resented by a joint tree, further by an associated surface of it.
在联树模型的基础上，把图在曲面上的嵌入用其联树，也即其关联曲面来表示。
An uncorrelated kernel extension of graph embedding which provides a unified method for computing all kinds of uncorrelated kernel dimensionality reduction algorithms is proposed.
提出统计不相关的核化图嵌入算法，为求解各种统计不相关的核化降维算法提供了一种统一方法。
Besides, the relation between uncorrelated kernel extension of graph embedding and kernel extension of graph embedding is revealed.
另外，揭示了统计不相关的核化图嵌入与已有的核化图嵌入的内在关系。
In this paper, We obtain the total genus polynomials for two new classes of 4-regular graphs by using the joint tree model of a graph embedding introduced by Yanpei Liu.
本文利用刘彦佩提出的嵌入的联树模型，得出了两类新的四正则图的完全亏格多项式，并推导出已有结果的两类图的完全亏格多项式。
In this paper, We obtain the total genus polynomials for two new classes of 4-regular graphs by using the joint tree model of a graph embedding introduced by Yanpei Liu.
在刘彦佩提出的联树法的基础上，通过分类一类新图类的可定向嵌入曲面求出了这类图类的可定向嵌入的亏格分布。
The two dimensional bandwidth problem is to determine an embedding of graph G in a grid graph in the plane such that the longest edges are as short as possible.
二维带宽问题是：确定图G在平面格子上的一个嵌入，使得最长边尽可能短。
The two-dimensional bandwidth problem is to find an embedding of graph G in a grid graph in the plane so that the longest edges are as short as possible.
二维带宽问题是将图G的顶点嵌入平面格子图，使其最长的连线尽可能短。
The experimental results on ORL, YALE and FERET face databases show that the proposed uncorrelated kernel extension of graph embedding method is better than other methods in terms of recognition rate.
通过在ORL，YALE和FERET人脸库上的实验结果表明，提出的具有统计不相关的核化图嵌入算法在识别率方面好于已有的核算法。
The experimental results on ORL, YALE and FERET face databases show that the proposed uncorrelated kernel extension of graph embedding method is better than other methods in terms of recognition rate.
通过在ORL，YALE和FERET人脸库上的实验结果表明，提出的具有统计不相关的核化图嵌入算法在识别率方面好于已有的核算法。
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