Circumferences and Graphic Ramsey Theory

摘要：研究人员研究了图论中的两个领域：(1)图拉姆齐理论，(2)结构图论。这个建议的基本目标是研究围绕三个猜想的问题：3连通平面图的周长上的月球-莫泽猜想，Chvall韧性猜想，以及Burr-Erdos Ramsey线性有界猜想。图论是一个相对较新的数学分支，在许多领域都有应用，如计算机科学、电信和交通。所描述的问题是图论中的主要问题。除了它们的理论意义之外，这里讨论的许多问题都是计算机科学家感兴趣的。

Abstract: The investigator studies two areas in graph theory: (1) Graphic Ramsey Theory, and (2) Structural Graph Theory. The basic goal of this proposal is to work on problems surrounding three conjectures: the Moon-Moser conjecture on circumferences of a 3-connected planar graph, the Chvatal Toughness conjecture, and the Burr-Erdos Ramsey Linear Bound conjecture.Graph theory is a relative new branch of mathematics that has applications in many areas, such as computer science, telecommunications, and transportation. The problems described are major problems in graph theory. In addition to their theoretic significance, many of the questions addressed here are of interest for computer scientists.