6 papers · 1 filter
Maker Breaker Games on a Budget
Sebastian Lüderssen, Fabien Nießen, Silas Rathke
The Maker Breaker Triangle Game involves two players, Maker and Breaker, who alternately claim 1 and edges of , respectively. Maker's goal is to claim all three edges of a…
No extremal square-free words over alphabets of size at least 5
Eng Keat Hng, Silas Rathke
A word over an alphabet contains a square if it has a subword of the form where is a word. A word is \emph{extremal square-free} if it does not contain a s…
The maximum diameter of -dimensional simplicial complexes
Stefan Glock, Olaf Parczyk, Silas Rathke +1
For every fixed dimension and sufficiently large , we determine the maximum possible diameter of a strongly connected -dimensional simplicial complex on vertices. Thi…
Spanning Components and Surfaces Under Minimum Vertex Degree
Jack Allsop, Ander Lamaison, Richard Lang +1
We study minimum vertex-degree conditions in 3-uniform hypergraphs for (tight) spanning components and (combinatorial) surfaces. Our main results show that a 3-uniform hypergraph $…
The maximum diameter of 2-dimensional simplicial complexes
Olaf Parczyk, Silas Rathke, Tibor Szabó
We study a problem of Santos about the largest possible diameter of a -dimensional (abstract) simplicial complex on vertices. For dimension 2, we determine the exact value o…
On the chromatic number of powers of subdivisions of graphs
Michael Anastos, Simona Boyadzhiyska, Silas Rathke +1
For a given graph , we define its \emph{th subdivision} as the graph obtained from by replacing every edge by a path of length . We also define the \emph{th p…