Thesiss

Network design problems deal with settings where the goal is to design a network (i.e., find a subgraph of a given graph) that satisfies certain connectivity requirements. Each requirement is in the form of connecting (or, more generally, providing large connectivity between) a …

In this thesis we study two colouring problems on planar graphs. The main technique we use is the Discharging Method, which was used to prove the Four Colour Theorem. The first problem we study is a conjecture of Steinberg which states that every planar graph without 4 and 5-cyc…