Splittings of Binomial Edge Ideals

A graph is a collection of nodes or points, called vertices, along with a collection of objects called edges, which connect some of the vertices. Graphs can be used to model a number of real world applications. For example, the world wide web can be represented by a node for each website, and an edge between vertices represents a link from one website to another. Understanding the structure of graphs can help us understand the structure of the web, and to help us ensure connections between various websites. In the last two decades, an area of mathematics, called combinatorial commutative algebra, has been developed to study graphs using algebraic tools. One associates with a given graph an algebraic object called an ideal. There are many different ways to do this; in the project, we are interested in studying algebra objects called binomial edge ideals.COur specific project is to understand if the these binomial edge ideals can be broken down (or “split”) into smaller binomial edge ideals; the hope is that these smaller ideals will be related to subsets of the original graph and further, give information about the larger ideas and graphs.

Faculty Supervisor:

Adam Van Tuyl

Student:

Partner:

Indian Institute of Technology Madras

Discipline:

Mathematics

Sector:

Other; Information and Communications Technology

University:

McMaster University

Program: