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math.CO2018
Erdős-Pósa property for labelled minors: 2-connected minors
Henning Bruhn, Felix Joos, Oliver Schaudt
In the 1960s, Erdős and Pósa proved that there is a packing-covering duality for cycles in graphs. As part of the graph minor project, Robertson and Seymour greatly extended this:…
math.CO2016
Approximately coloring graphs without long induced paths
Maria Chudnovsky, Oliver Schaudt, Sophie Spirkl +2
It is an open problem whether the 3-coloring problem can be solved in polynomial time in the class of graphs that do not contain an induced path on vertices, for fixed . We…
math.CO2013
The union-closed sets conjecture almost holds for almost all random bipartite graphs
Henning Bruhn, Oliver Schaudt
Frankl's union-closed sets conjecture states that in every finite union-closed set of sets, there is an element that is contained in at least half of the member-sets (provided ther…