Extremal problems in ordered graphs
نویسنده
چکیده
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 [12] 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 [7] by establishing an upper bound on the number of edges allowed if the forbidden graphs fit a generalized notion of a matching.
منابع مشابه
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ورودعنوان ژورنال:
- CoRR
دوره abs/0907.2479 شماره
صفحات -
تاریخ انتشار 2009