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Well-Quasi-Ordering By The Induced-Minor Relation, Chanun Lewchalermvongs

LSU Doctoral Dissertations

Robertson and Seymour proved Wagner's Conjecture, which says that finite graphs are well-quasi-ordered by the minor relation. Their work motivates the question as to whether any class of graphs is well-quasi-ordered by other containment relations. This dissertation is concerned with a special graph containment relation, the induced-minor relation. This dissertation begins with a brief introduction to various graph containment relations and their connections with well-quasi-ordering. In the first chapter, we discuss the results about well-quasi-ordering by graph containment relations and the main problems of this dissertation. The graph theory terminology and preliminary results that will be used are presented in …