This project will examine systems of intervals on the real number line and their associated overlap graphs. An overlap graph is a graph where each vertex represents an interval, and an edge represents that two intervals intersect, but neither is contained in the other (in this case we say the intervals overlap). This project will initially focus on studying the properties of overlap graphs when specific combinations of intervals do not appear in the interval system. This will allow us to define hereditary subclasses of interval systems and the properties of the related overlap graphs classes. Among other questions, we will investigate the relations between these classes and permutation graphs, a well-known subclass of overlap graphs.
Eamonn Kashyap is a student at RMIT University who has recently completed his third year in Bachelor of Science majoring in Statistics. From a young age, Eamonn has been attracted to mathematics and logic. While studying at RMIT, Eamonn has developed a particular interest in group theory, Bayesian statistics and graph algorithms. With this in mind, Eamonn has decided to pursue an honours degree to expand his understanding in mathematics and statistics.