可定向曲面上具有较短不可收缩圈图嵌入的唯一性

拓扑图论中的一个基本问题就是要决定图在一个(可定向)曲面上的嵌入之数目(既嵌入的柔性问题).H.Whitney的经典结果表明:一个3-连通图至多有一个平面嵌入;C.Thomassen的LEW-嵌入(大边宽度)理论将这一结果推广到一般的可定向曲面.本文给出了几个关于一般可定向曲面上嵌入图的唯一性定理.结果表明:一些具有大的面迹的可定向嵌入仍然具有唯一性.这在本质上推广了C.Thomassen在LEW-嵌入方面的工作.     

超曲面上极小与极小凸点的分布

本文继续文［1］中的讨论,给出超曲面上点的极小与极小凸性更一般的判别方式,并且对超曲面上极小与极小凸点的分布有了更深刻的认识.作为应用,还证明了超曲面上一个极小点的传递性定理.     

超曲面上极小与极小凸点的分布

本文继续文［１］中的讨论,给出超曲面上点的极小与极小凸性更一般的判别方式,并且对超曲面上极小与极小凸点的分布有了更深刻的认识．作为应用,还证明了超曲面上一个极小点的传递性定理．     

一类具有任意次数的参数多项式极小曲面

极小曲面是在几何造型设计中有着重要应用的一类特殊曲面.本文从几何造型的视角提出一类次数任意的参数多项式极小曲面.所提出的极小曲面具有显式的参数表示,并具有一些重要的几何性质,如对称性、包含直线和自交性.根据几何性质,本文将该参数多项式极小曲面划分为4类:n=4k+1,n=4k+2,n=4k+3,n=4+4,其中n是极小曲面的次数,k是正整数.本文给出与之相对应的共轭极小曲面的显式参数形式,并实现其等距变形.     

关于3维欧氏空间中一族嵌入极小曲面的一个注记

本文证明了在 Ｄ． Ｈｏｆｆｍａｎ和 Ｗ．Ｈ． Ｍｅｅｋｓ， Ⅲ［４］给出的 ３维欧氏空间的一族嵌入极小曲面中，每一个曲面与其自身的和曲面是平凡的极小核心．     

一类具有纤维化的一般型极小曲面的斜率

设 S 是一般型极小的代数曲面,f 是纤维化,则有自然的正合列 π_1(F)→π_1(S)→π→1.在本文中我们证明,如果 f 为非局部平凡,且 S 具有一个2阶挠元,那么λ(f)≥4-1/(g-1),这里 g 是 f 的纤维 F 的亏格.     

双曲空间中旋转对称的极小超曲面

本文给出了双曲空间Hⁿ中旋转对称的极小超曲面的微分方程,对这类超曲面进行了分类,它们是Hⁿ中的超平面或广义悬链面,而每个广义悬链面被夹在两个平行的超平面之间,且以这两个超平面为渐近平面.     

一类极小曲面的不存在性

本文考虑三维 Euclid 空间 R~3中拓扑型为球面的有限全曲率完备嵌入极小曲面.通过对伪嵌入极小曲面的研究,证明了一类嵌入极小曲面的不存在性,并明确了伪嵌入与嵌入极小曲面的差异.     

Forbidden Induced Subgraphs for Toughness

Let be a family of connected graphs. A graph G is said to be ‐free if G is H‐free for every graph H in . We study the relation between forbidden subgraphs in a connected graph G and the resulting toughness of G. In particular, we consider the problem of characterizing the graph families such that every large enough connected ‐free graph is t‐tough. In this article, we solve this problem for every real positive number t. © 2012 Wiley Periodicals, Inc. J. Graph Theory 73: 191–202, 2013     

A Survey on the Computational Complexity of Coloring Graphs with Forbidden Subgraphs

For a positive integer k, a k‐coloring of a graph is a mapping such that whenever . The Coloring problem is to decide, for a given G and k, whether a k‐coloring of G exists. If k is fixed (i.e., it is not part of the input), we have the decision problem k‐Coloring instead. We survey known results on the computational complexity of Coloring and k‐Coloring for graph classes that are characterized by one or two forbidden induced subgraphs. We also consider a number of variants: for example, where the problem is to extend a partial coloring, or where lists of permissible colors are given for each vertex.     

Forbidden ordered subgraph vs. forbidden subgraph characterizations of graph classes

We show that the minimum set of unordered graphs that must be forbidden to get the same graph class characterized by forbidding a single ordered graph is infinite. © 1999 John Wiley & Sons, Inc. J Graph Theory 30: 71–76, 1999     

Universal Graphs with Forbidden Subgraphs and Algebraic Closure

We apply model theoretic methods to the problem of existence of countable universal graphs with finitely many forbidden connected subgraphs. We show that to a large extent the question reduces to one of local finiteness of an associated “algebraic closure” operator. The main applications are new examples of universal graphs with forbidden subgraphs and simplified treatments of some previously known cases.     

Forbidden Subgraphs of the Odd‐Distance Graph

In [2], on page 252 the following logical terminal inexactitude was made: “...the existence of a K₄ is the only obstruction. That is, every finite K₄‐free graph can be represented by odd‐distances in the plane.” In this note we correct this erroneous claim by showing that W₅, the 5‐wheel, see Figure 1, is not a subgraph of .     

Forbidden Pairs of Disconnected Graphs Implying Hamiltonicity

Let H be a given graph. A graph G is said to be H‐free if G contains no induced copies of H. For a class of graphs, the graph G is ‐free if G is H‐free for every . Bedrossian characterized all the pairs of connected subgraphs such that every 2‐connected ‐free graph is hamiltonian. Faudree and Gould extended Bedrossian's result by proving the necessity part of the result based on infinite families of non‐hamiltonian graphs. In this article, we characterize all pairs of (not necessarily connected) graphs such that there exists an integer n₀ such that every 2‐connected ‐free graph of order at least n₀ is hamiltonian.     

Forbidden subgraphs that imply hamiltonian‐connectedness*

It is proven that if G is a 3‐connected claw‐free graph which is also H₁‐free (where H₁ consists of two disjoint triangles connected by an edge), then G is hamiltonian‐connected. Also, examples will be described that determine a finite family of graphs such that if a 3‐connected graph being claw‐free and L‐free implies G is hamiltonian‐connected, then L . © 2002 Wiley Periodicals, Inc. J Graph Theory 40: 104–119, 2002     

有关极小曲面问题

本文阐述了有关极小曲面问题的研究状况以及主要研究方法 ,指出目前存在尚未解决的一些问题 .