Extremal Problems in Ordered Graphs

Download or read book Extremal Problems in Ordered Graphs written by Craig Weidert and published by . This book was released on 2009 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis we consider ordered graphs (that is, graphs with a fixed linear ordering on their vertices). We summarize and further investigations on the number of edges an ordered graph may have while avoiding a fixed forbidden ordered graph as a subgraph. In particular, we take a step toward confirming a conjecture of Pach and Tardos regarding the number of edges allowed when the forbidden pattern is a tree by establishing an upper bound for a particular ordered graph for which existing techniques have failed. We also generalize a theorem of Geneson by establishing an upper bound on the number of edges allowed if the forbidden graphs fit a generalized notion of a matching.