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Van der Waerden's theorem states that any coloring of
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A common technique to characterize hereditary graph classes is to exhibit their minimal obstructions. Sometimes, the set of minimal obstructions might be infinite, or too complicated to describe. For instance, for any |
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A well-known conjecture of Burr and Erdős asserts that the Ramsey number |
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We determine the maximum number of copies of |
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Order types are a combinatorial classification of finite point sets used in discrete and computational geometry. This talk will give an introduction to these objects and their analogue for the projective plane, with an emphasis on their symmetry groups. This is joint work with Emo Welzl. |
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In computer science, random expressions are commonly used to analyze algorithms, either to study their average complexity, or to generate benchmarks to test them experimentally. In general, these approaches only consider the expressions as purely syntactic trees, and completely ignore their semantics — i.e. the mathematical object represented by the expression. However, two different expressions … |
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We study the problem of maximizing a continuous DR-submodular function that is not necessarily smooth. We prove that the continuous greedy algorithm achieves an guarantee when the function is monotone and Hölder-smooth, meaning that it admits a Hölder-continuous gradient. For functions that are non-differentiable or non-smooth, we propose a variant of the mirror-prox algorithm that … |
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