Using unavoidable set of trees to generalize Kruskal's theorem

Extension of the Douady-Hubbard's Theorem on Connectedness of the Mandelbrot Set to Symmetric Polynimials

Unavoidable trees and forests in graphs

Classic results from extremal graph theory state that if certain graphs are made large enough, unavoidable substructures appear. Here we will cover this type of problem for specific graphs when these substructures are certain trees or forests. After giving a summary on related results, the following two extremal main problems are presented: For a given family of same-order trees including the s...

Learning Small Trees and Graphs that Generalize

In this Thesis we study issues related to learning small tree and graph formed classifiers. First, we study reduced error pruning of decision trees and branching programs. We analyze the behavior of a reduced error pruning algorithm for decision trees under various probabilistic assumptions on the pruning data. As a result we get, e.g., new upper bounds for the probability of replacing a tree t...

An Unavoidable Set of D-Reducible Configurations

We give a new proof of the four-color theorem by exhibiting an unavoidable set of 2822 D-reducible configurations. The existence of such a set had been conjectured by several researchers including Stromquist [18], Appel and Haken [2] and Robertson, Sanders, Seymour and Thomas [15].

Decision trees do not generalize to new variations

The family of decision tree learning algorithms is among the most widespread and studied. Motivated by the desire to develop learning algorithms that can generalize when learning highly varying functions such as those presumably needed to achieve artificial intelligence, we study some theoretical limitations of decision trees. We demonstrate formally that they can be seriously hurt by the curse...