Extremal problems in ordered graphs

Details Extremal problems in ordered graphs Extremal problems in ordered graphs

2009-07-15

arxiv.org/abs/0907.2479v1

Computer Science

Discrete Mathematics

Thesis for Master Degree, Simon Fraser University

Scientific paper

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.

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