Circumferences and Graphic Ramsey Theory

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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.