3 papers
math.CO2025
String Graphs: Product Structure and Localised Representations
Nikolai Karol
We investigate string graphs through the lens of graph product structure theory, which describes complicated graphs as subgraphs of strong products of simpler building blocks. A gr…
math.CO2025
Structure of -Matching-Planar Graphs
Kevin Hendrey, Nikolai Karol, David R. Wood
For , we define a simple topological graph (that is, a graph drawn in the plane such that every pair of edges intersect at most once, including endpoints) to be…
math.CO2024
Treewidth 2 in the Planar Graph Product Structure Theorem
Marc Distel, Kevin Hendrey, Nikolai Karol +2
We prove that every planar graph is contained in for some graphs and both with treewidth 2. This resolves a question of Liu, Norin and W…