Some Topics concerning Graphs, Signed Graphs and Matroids
Vaidyanathan Sivaraman · OhioLink ETD Center (Ohio Library and Information Network) · 2012
I would like to thank Prof. Neil Robertson for sharing his deep understanding of structural aspects of graphs.I have learned a lot about graphs from the numerous weekly meetings I have enjoyed with him.His penetrating questions and constructive comments have streamlined many of the arguments presented in this dissertation.His personal accounts of the Fantastic Four -Graph Minors, Hadwiger's Conjecture for k = 6, Four Color Theorem, and Strong Perfect Graph Theorem, were very interesting, and gave me a very clear picture of how research progresses in phases.Daniel Slilaty gave a series of talks here at Ohio State during November 2007, which is the basis for many of the topics in this thesis.He first defined matroids for me and pointed to Oxley's book for further study.I have immensely benefitted from several discussions with Thomas Zaslavsky.My first encounter with serious combinatorics was in a course by Prof. Ákos Seress.He is a wonderful teacher and his spectacular treatment of matching theory eventually led me to topics related to transversal matroids.I have learned several probabilistic techniques from Prof.