Frontiers in Mathematical Sciences
University of Isfahan - January 1-3, 2020
An Introduction to Ramsey TheorySpeaker:
Maryam Shahsiah, University of Khansar
Date, Time, and Venue: Friday, January 3 | 11:15-12:00 | Hall 1Abstract:
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 well-organized 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.