Abstract: Simply put, a graph is nothing but a set of points ("vertices"), along with edges which connect them. A planar graph is a special type of graph- one where the edges do not cross each other ( i.e., meet only at the vertices). In this talk, we will discuss an interesting problem in planar graph theory- that of trying to colour the vertices with as few colours as possible, subject to the condition that no two adjacent vertices have the same colour. We will go on to prove the Five Colour Theorem, which says that for any planar graph, there exists such a colouring utilising only five colours. We will further discuss the Four Colour "Conjecture".
The only prerequisites are curiosity and an eagerness to learn!
School of Mathematical Sciences
NISER, PO- Bhimpur-Padanpur, Via- Jatni, District- Khurda, Odisha, India, PIN- 752050