73 citations · 178 across the 49 of their papers we have counts for
45 papers · 1 filter
Strong coloring numbers of grids
Piotr Micek, Torsten Ueckerdt
For positive integers and , the -dimensional grid of side length is the graph with vertex set , in which two vertices are adjacent if they differ by $…
The Density Formula: One Lemma to Bound Them All
Michael Kaufmann, Boris Klemz, Kristin Knorr +3
We introduce the Density Formula for (topological) drawings of graphs in the plane or on the sphere, which relates the number of edges, vertices, crossings, and sizes of cells in t…
Shallow Hitting Edge Sets in Uniform Hypergraphs
Tim Planken, Torsten Ueckerdt
A subset of the edges of a graph or hypergraph is hitting if covers each vertex of at least once, and is -shallow if it covers each vertex of at most tim…
Clustered independence and bounded treewidth
Kolja Knauer, Torsten Ueckerdt
A set of vertices of a graph is a -clustered set if it induces a subgraph with components of order at most each, and denotes the size of a larges…
Cops and Robber -- When Capturing is not Surrounding
Paul Jungeblut, Samuel Schneider, Torsten Ueckerdt
We consider "surrounding" versions of the classic Cops and Robber game. The game is played on a connected graph in which two players, one controlling a number of cops and the other…
Tight bound on treedepth in terms of pathwidth and longest path
Meike Hatzel, Gwenaël Joret, Piotr Micek +3
We show that every graph with pathwidth strictly less than that contains no path on vertices as a subgraph has treedepth at most . The bound is best possible up to…