Shantanam, Abhinav2016-08-242016-08-242016-08-242016-08-18http://hdl.handle.net/10012/10682This thesis shows that, for every positive integer $n \geq 5$, there exists a positive integer $N$ such that every $5-$connected graph with at least $N$ vertices has a minor isomorphic to one of thirty explicitly defined $5-$connected graphs $H_1(n), ..., H_{30}(n)$, each with at least $n$ vertices.enunavoidable minors5-connectedMaster Thesis