2 citations · 2 across the 5 of their papers we have counts for
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Beating the Ahlswede--Khachatrian bound for the Erdős--Frankl--Pach problem
Tuan Tran, Zixiang Xu
In the 1980s, Erdős and, independently, Frankl and Pach conjectured that, for sufficiently large , every -uniform family on with VC-dimension has siz…
Rainbow cycles in properly edge-colored graphs
Jaehoon Kim, Joonkyung Lee, Hong Liu +1
We prove that every properly edge-colored -vertex graph with average degree at least contains a rainbow cycle, improving upon bound due to To…
Exponential decay of intersection volume with applications on list-decodability and Gilbert-Varshamov type bound
Jaehoon Kim, Hong Liu, Tuan Tran
We give some natural sufficient conditions for balls in a metric space to have small intersection. Roughly speaking, this happens when the metric space is (i) expanding and (ii) we…
Unavoidable hypergraphs
M. Bucić, N. Draganić, B. Sudakov +1
The following very natural problem was raised by Chung and Erdős in the early 80's and has since been repeated a number of times. What is the minimum of the Turán number $\text{ex}…
Dense induced bipartite subgraphs in triangle-free graphs
Matthew Kwan, Shoham Letzter, Benny Sudakov +1
The problem of finding dense induced bipartite subgraphs in -free graphs has a long history, and was posed 30 years ago by Erdős, Faudree, Pach and Spencer. In this paper, we ob…
Nearly-linear monotone paths in edge-ordered graphs
Matija Bucic, Matthew Kwan, Alexey Pokrovskiy +3
How long a monotone path can one always find in any edge-ordering of the complete graph ? This appealing question was first asked by Chvátal and Komlós in 1971, and has since…