Regularity inheritance in pseudorandom graphs
Peter Allen, Julia B\"ottcher, Jozef Skokan, Maya Stein
TL;DR
This paper improves the understanding of regularity inheritance in bijumbled graphs, providing new lemmas that enhance counting and regularity results in sparse graph settings.
Contribution
It introduces improved one-sided and two-sided regularity inheritance lemmas for bijumbled graphs, advancing the sparse regularity method.
Findings
Enhanced regularity inheritance lemmas for bijumbled graphs
Improved $H$-counting lemmas for subgraphs of bijumbled graphs
Advancement in sparse regularity method techniques
Abstract
Advancing the sparse regularity method, we prove one-sided and two-sided regularity inheritance lemmas for subgraphs of bijumbled graphs, improving on results of Conlon, Fox and Zhao [Adv. Math. 256 (2014), 206--290]. These inheritance lemmas also imply improved -counting lemmas for subgraphs of bijumbled graphs, for some .
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Videos
Regularity Inheritance in Pseudorandom Graphs· youtube
Taxonomy
TopicsLimits and Structures in Graph Theory · Complexity and Algorithms in Graphs · Cooperative Communication and Network Coding