1 citations · 6 across the 31 of their papers we have counts for
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Merino-Welsh inequalities for matroids with controlled lattices of cyclic flats
Kolja Knauer, Leonardo Martínez-Sandoval, Criel Merino
Beke, Csáji, Csikvári, and Pituk showed that the Merino--Welsh quotient can be arbitrarily large, so the multiplicative Merino-Welsh inequality…
Rings are -bounded
Sara Asensio, Ignacio García-Marco, Kolja Knauer
We prove that there is a function such that for the zero-divisor graph of any ring , if the clique number is finite. On the on…
Neither simpliciality nor mutation connectivity: conjectures of Las Vergnas and Cordovil-Las Vergnas fail
Qiyuan Gu, Kolja Knauer
We construct a simple rank- oriented matroid on elements with no simplicial tope, disproving the Las Vergnas simplex conjecture from 1980. We then show that the mutation gr…
Logarithmic basis number of graphs and regular matroids
Kolja Knauer
The basis number of a graph is the minimum edge-congestion of a basis of its cycle space. We prove that every finite -vertex multigraph satisfies ,…
Coloring semiminimal Cayley Graphs
Ignacio García-Marco, Kolja Knauer, Giuliamaria Menara
In 1978 Babai raised the question whether all semiminimal Cayley graphs have bounded chromatic number. In this paper we show that semiminimal Cayley graphs of abelian and generaliz…
Embracing exchange sequences and oriented matroid polyhedron diameter
Kristóf Bérczi, Kolja Knauer, Luis Pedro Montejano +1
We reduce the embracing exchange distance of bases of oriented matroids to the metric of oriented matroid polyhedra. This allows us to disprove recent conjectures of Caoduro, Khoda…