1 citations · 2 across the 3 of their papers we have counts for
6 papers
The Dimension of the Negative Cycle Vectors of Signed Graphs
Alex Schaefer, Thomas Zaslavsky
A "signed graph" is a graph where the edges are assigned sign labels, either "" or "". The sign of a cycle is the product of the signs of its edges. Let $\mathrm{SpecC}(Γ…
Balanced Non-Transitive Dice II: Tournaments
Alex Schaefer
We further study sets of labeled dice in which the relation "is a better die than" is non-transitive. Focusing on sets with an additional symmetry we call "balance," we prove that…
Graphs that contain multiply transitive matchings
Alex Schaefer, Eric Swartz
Let be a finite, undirected, connected, simple graph. We say that a matching is a \textit{permutable -matching} if contains edges and the sub…
Balanced Non-Transitive Dice
Alex Schaefer, Jay Schweig
We study triples of labeled dice in which the relation "is a better die than" is non-transitive. Focusing on such triples with an additional symmetry we call "balance," we prove th…
The Negative Cycle Vectors of Signed Complete Graphs
Alex Schaefer
A signed graph is a graph where the edges are assigned labels of either "" or "". The sign of a cycle in the graph is the product of the signs of its edges. We equip each sig…
Strongly connectable digraphs and non-transitive dice
Simon Joyce, Alex Schaefer, Douglas B. West +1
We give a new proof of the theorem of Boesch-Tindell and Farzad-Mahdian-Mahmoodian-Saberi-Sadri that a directed graph extends to a strongly connected digraph on the same vertex set…