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math.CO2025
Unavoidable pivot-minors in graphs of large rank-depth
Jungho Ahn, Kevin Hendrey, O-joung Kwon +1
Shrub-depth and rank-depth are related graph parameters that are dense analogs of tree-depth. We prove that for every positive integer , every graph of sufficiently large rank-d…
math.CO2025
The Erdős-Pósa property for circle graphs as vertex-minors
Rutger Campbell, J. Pascal Gollin, Meike Hatzel +4
We prove that for any circle graph with at least one edge and for any positive integer , there exists an integer so that every graph either has a vertex-minor…