Michael Kaufmann

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math.CO2026

On t-colorable k-plane drawings

Miriam Goetze, Michael Kaufmann, Soeren Terziadis

In this work, we introduce $t$ -colorable $k$ -plane drawings, that is, drawings of graphs with a $t$ -edge-coloring where every edge is crossed by at most $k$ edges of each color. We…

math.CO2024

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…

math.CO2024

Improving the Crossing Lemma by Characterizing Dense 2-Planar and 3-Planar Graphs

Aaron BÃ¼ngener, Michael Kaufmann

The classical Crossing Lemma by Ajtai et al.~and Leighton from 1982 gave an important lower bound of $c \frac{m ^{3}}{n ^{2}}$ for the number of crossings in any drawing of a given graph…

math.CO2024

On $k$ -planar Graphs without Short Cycles

Michael A. Bekos, Prosenjit Bose, Aaron BÃ¼ngener +6

We study the impact of forbidding short cycles to the edge density of $k$ -planar graphs; a $k$ -planar graph is one that can be drawn in the plane with at most $k$ crossings per edg…

On t-colorable k-plane drawings

The Density Formula: One Lemma to Bound Them All

Improving the Crossing Lemma by Characterizing Dense 2-Planar and 3-Planar Graphs

On k-planar Graphs without Short Cycles

On $k$ -planar Graphs without Short Cycles