For r-uniform linear hypergraphs with nonnegative Lin-Lu-Yau curvature, edge-connectivity equals minimum incidence degree, while nonlinear examples violate this with arbitrarily large gaps.
Edge-connectivity and non-negative Lin-Lu-Yau curvature
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
By definition, the edge-connectivity of a connected graph is no larger than its minimum degree. In this paper, we prove that the edge connectivity of a finite connected graph with non-negative Lin-Lu-Yau curvature is equal to its minimum degree. This answers an open question of Chen, Liu and You. Notice that our conclusion would be false if we did not require the graph to be finite. We actually classify all connected graphs with non-negative Lin-Lu-Yau curvature and edge-connectivity smaller than their minimum degree. In particular, they are all infinite.
citation-role summary
background 1
citation-polarity summary
fields
math.CO 1years
2026 1verdicts
CONDITIONAL 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
Edge-connectivity and LLY curvature of hypergraphs
For r-uniform linear hypergraphs with nonnegative Lin-Lu-Yau curvature, edge-connectivity equals minimum incidence degree, while nonlinear examples violate this with arbitrarily large gaps.