Gwenaël Joret, Packing and covering balls in graphs excluding a minor

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In 2007, Chepoi, Estellon, and Vaxès conjectured that there exists a universal constant $c>0$ such that the following holds for every positive integers $r$ and $k$, and every planar graph $G$: Either $G$ contains $k$ vertex-disjoint balls of radius $r$, or there is a subset of vertices of size at most $c k$ meeting all

Sebastian Siebertz, Rank-width meets stability

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Forbidden graph characterizations provide a convenient way of specifying graph classes, which often exhibit a rich combinatorial and algorithmic theory. A prime example in graph theory are classes of bounded tree-width, which are characterized as those classes that exclude some planar graph as a minor. Similarly, in model theory, classes of structures are characterized by