6 papers
Colorings of oriented planar graphs avoiding a monochromatic subgraph
Helena Bergold, Winfried Hochstättler, Raphael Steiner
For a fixed simple digraph and a given simple digraph , an -free -coloring of is a vertex-coloring in which no induced copy of in is monochromatic. We stud…
Complete Acyclic Colorings
Stefan Felsner, Winfried Hochstättler, Kolja Knauer +1
We study two parameters that arise from the dichromatic number and the vertex-arboricity in the same way that the achromatic number comes from the chromatic number. The adichromati…
The NL-flow polynomial
Barbara Altenbokum, Winfried Hochstättler, Johanna Wiehe
In 1982 Víctor Neumann-Lara introduced the dichromatic number of a digraph as the smallest integer such that the vertices of can be colored with colors and each…
The Varchenko Determinant for Oriented Matroids
Winfried Hochstättler, Volkmar Welker
We generalize the Varchenko matrix of a hyperplane arrangement to oriented matroids. We show that the celebrated determinant formula for the Varchenko matrix, first proved by Varch…
Sticky matroids and Kantor's Conjecture
Winfried Hochstättler, Michael Wilhelmi
We prove the equivalence of Kantor's Conjecture and the Sticky Matroid Conjecture due to Poljak und Turzík.
The game colouring number of powers of forests
Stephan Dominique Andres, Winfried Hochstättler
We prove that the game colouring number of the -th power of a forest of maximum degree is bounded from above by \[\frac{(Δ-1)^m-1}{Δ-2}+2^m+1,\] which improves the best…