2 papers
math.CO2024
Matroid colorings of KKM covers
Daniel McGinnis
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…
math.CO2024
Using the KKM theorem
Daniel McGinnis, Shira Zerbib
The KKM theorem, due to Knaster, Kuratowski, and Mazurkiewicz in 1929, is a fundamental result in fixed-point theory, which has seen numerous extensions and applications. In this p…