3 papers
math.CO2026
An equality for balanced digraphs
Darij Grinberg, Benjamin Liber
Consider a directed multigraph that is balanced (i.e., at each vertex, the indegree equals the outdegree). Let be its set of arcs. Fix an integer . Let be a vertex o…
math.CO2026
Degree Sequences vs. Forests in Finite Graphs
Benjamin Liber
We prove two conjectures of Shteiner and Shteyner stating that for an undirected graph , the number of degree sequences arising from its spanning subgraphs is at least the…
math.CO2025
On the Independence Numbers of the Cyclic Van der Waerden Hypergraphs
Benjamin Liber
Building upon the work of Berglund (2018), we establish a method for constructing subsets such that does not contain any -term cyclic arithmeti…