The authors prove that any point configuration whose convex-hull intersection combinatorics is captured by a Radon pair yields a Fan-type covering or labeling theorem for the sphere, and derive colorful, continuous, and (Z/2)^2-equivariant versions.
Matroid colorings of KKM covers
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We prove a KKM-type theorem for matroid colored families of set coverings of a polytope. This generalizes Gale's colorful KKM theorem as well as recent sparse-colorful variants by Sober\'on, and McGinnis and Zerbib.
citation-role summary
background 1
citation-polarity summary
fields
math.CO 1years
2025 1verdicts
CONDITIONAL 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
Covering and labeling generalizations of the Borsuk-Ulam theorem
The authors prove that any point configuration whose convex-hull intersection combinatorics is captured by a Radon pair yields a Fan-type covering or labeling theorem for the sphere, and derive colorful, continuous, and (Z/2)^2-equivariant versions.