7 citations · 44 across the 35 of their papers we have counts for
9 papers · 1 filter
Hat guessing numbers of strongly degenerate graphs
Charlotte Knierim, Anders Martinsson, Raphael Steiner
Assume players are placed on the vertices of a graph . The following game was introduced by Winkler: An adversary puts a hat on each player, where each hat has a colour…
Edge Partitions of Complete Geometric Graphs (Part 2)
Oswin Aichholzer, Johannes Obenaus, Joachim Orthaber +5
Recently, the second and third author showed that complete geometric graphs on vertices in general cannot be partitioned into plane spanning trees. Building up on this wor…
Tight bounds for divisible subdivisions
Shagnik Das, Nemanja Draganić, Raphael Steiner
Alon and Krivelevich proved that for every -vertex subcubic graph and every integer there exists a (smallest) integer such that every -minor contai…
Improved lower bound for the list chromatic number of graphs with no minor
Raphael Steiner
Hadwiger's conjecture asserts that every graph without a -minor is -colorable. It is known that the exact version of Hadwiger's conjecture does not extend to list color…
Asymptotic Equivalence of Hadwiger's Conjecture and its Odd Minor-Variant
Raphael Steiner
Hadwiger's conjecture states that every -minor free graph is -colorable. A qualitative strengthening of this conjecture raised by Gerards and Seymour, known as the Odd…
Zero sum cycles in complete digraphs
Tamás Mészáros, Raphael Steiner
Given a non-trivial finite Abelian group , let be the smallest integer such that for every labelling of the arcs of the bidirected complete graph of order $n(A)…
On coloring digraphs with forbidden induced subgraphs
Raphael Steiner
We prove a conjecture by Aboulker, Charbit and Naserasr by showing that every oriented graph in which the out-neighborhood of every vertex induces a transitive tournament can be pa…
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 minors in digraphs with given dichromatic number
Tamás Mészáros, Raphael Steiner
The dichromatic number of a digraph is the smallest for which it admits a -coloring where every color class induces an acyclic subgraph. Inspired by Hadwiger'…