Frontiers in Mathematical Sciences
7th Conference University of Isfahan  January 13, 2020 
Title:
An Introduction to Ramsey Theory
Speaker:
Maryam Shahsiah, University of Khansar
Date, Time, and Venue: Friday, January 3  11:1512:00  Hall 1
Abstract:
Ramsey theory refers to a large body of deep results in mathematics whose underlying
philosophy is captured succinctly by the statement that \every large system contains a large
wellorganized subsystem." This is an area in which a great variety of techniques from many
branches of mathematics are used and whose results are important not only to graph theory
and combinatorics but also to logic, analysis, number theory, and geometry. The cornerstone
of this area is Ramsey's theorem, which guarantees the existence of Ramsey numbers. De
termining or estimating Ramsey numbers is one of the central problems in combinatorics.
Besides the complete graph, the next most classical topic in this area concerns the Ramsey
numbers of sparse graphs, i.e., graphs with certain upper bound constraints on the degrees
of the vertices. One can naturally try to extend the sparse graph Ramsey results to hyper
graphs. In this talk, we present some obtained results on Ramsey number of sparse graphs
and hypergraphs. We specically present the relevant results on Ramsey number of loose
cycles.
