Pull-Push Method: A new approach to Edge-Isoperimetric Problems
Combinatorics
2023-07-12 v1
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.
Cite
@article{arxiv.2307.05289,
title = {Pull-Push Method: A new approach to Edge-Isoperimetric Problems},
author = {Sergei L. Bezrukov and Nikola Kuzmanovski and Jounglag Lim},
journal= {arXiv preprint arXiv:2307.05289},
year = {2023}
}