Work

Using the KKM theorem

Year: 2024

Type: preprint

Abstract: 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 paper we survey old and recent generalizations of the KKM theorem and their applications in the areas of piercing numbers, mass partition, fair division, and matching theory. We also give a few new results utilizing KKM-type theorems, and discuss related open problems.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2408.03921

Authors: McGinnis, Daniel, Zerbib, Shira

Institutions: Princeton University, Iowa State University

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: CAREER: KKM-Type Theorems for Piercing Numbers, Mass Partition, and Fair Division, G4098430822, G6671297155, Postdoctoral Fellowship: MSPRF: Discrete Geometry and Geometric Transversal Theory

OpenAlex ID: W4403965732

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