Pull-Push Method: A new approach to Edge-Isoperimetric Problems

Authors

• Sergei L. Bezrukov, University of Wisconsin
• Nikola Kuzmanovski, University of Nebraska-LincolnFollow
• Jounglag Lim, Clemson University

Document Type

Article

Date of this Version

7-11-2023

Citation

Published (2023) Discrete Mathematics, 346 (12), art. no. 113632, . DOI: 10.1016/j.disc.2023.113632

Comments

Used by permission.

Abstract

We prove a generalization of the Ahlswede-Cai local-global principle. A new technique to handle edge-isoperimetric problems is introduced which we call the pull-push method. Our main result includes all previously published results in this area as special cases with the only exception of the edge-isoperimetric problem for grids. With this we partially answer a question of Harper on local-global principles. We also describe a strategy for further generalization of our results so that the case of grids would be covered, which would completely settle Harper’s question.