3 papers
math.CO2026
When all directed cycles have the same weight
Eli Berger, Daniel Carter, Paul Seymour
A digraph is weightable if its edges can be weighted with real numbers such that the total weight in each directed cycle equals 1. There are several equivalent conditions: that…
math.CO2025
The minimal nonplanar strong digraphs
Stephen Bartell, Paul Seymour
Kuratowski's theorem says that the minimal (under subgraph containment) graphs that are not planar are the subdivisions of and of . Here we study the minimal (under…
math.CO2025
When all directed cycles have length three
Paul Seymour
We give a construction to build all digraphs with the property that every directed cycle has length three.