Extremal problems in ordered graphs
Discrete Mathematics
2009-07-16 v1
Abstract
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.
Cite
@article{arxiv.0907.2479,
title = {Extremal problems in ordered graphs},
author = {Craig Weidert},
journal= {arXiv preprint arXiv:0907.2479},
year = {2009}
}
Comments
Thesis for Master Degree, Simon Fraser University