37 citations · 102 across the 20 of their papers we have counts for
27 papers · 1 filter
A proof of the rational exponents conjecture
David Conlon, Oliver Janzer, Tao Jiang +5
The rational exponents conjecture of Erdős and Simonovits asserts that for every rational there exists a graph such that . We present a pr…
On the extremal number of incidence graphs
Jisun Baek, David Conlon, Joonkyung Lee
Given a graph and a natural number , the extremal number is the largest number of edges in an -vertex graph containing no copy of . In this paper,…
On norming systems of linear equations
Seokjoon Cho, David Conlon, Joonkyung Lee +2
A system of linear equations is said to be norming if a natural functional giving a weighted count for the set of solutions to the system can be used to define a n…
Around the positive graph conjecture
David Conlon, Joonkyung Lee, Leo Versteegen
A graph is said to be positive if the homomorphism density is non-negative for all weighted graphs . The positive graph conjecture proposes a characterisation of su…
Extremal numbers and Sidorenko's conjecture
David Conlon, Joonkyung Lee, Alexander Sidorenko
Sidorenko's conjecture states that, for all bipartite graphs , quasirandom graphs contain asymptotically the minimum number of copies of taken over all graphs with the same…
Domination inequalities and dominating graphs
David Conlon, Joonkyung Lee
We say that a graph dominates another graph if the number of homomorphisms from to any graph is dominated, in an appropriate sense, by the number of homomorphisms…
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…
Extended commonality of paths and cycles via Schur convexity
Jang Soo Kim, Joonkyung Lee
A graph is \emph{common} if the number of monochromatic copies of in a 2-edge-colouring of the complete graph is asymptotically minimised by the random colouring, or…
A proof of the Elliott-Rödl conjecture on hypertrees in Steiner triple systems
Seonghyuk Im, Jaehoon Kim, Joonkyung Lee +1
Hypertrees are linear hypergraphs where every two vertices are connected by a unique path. Elliott and Rödl conjectured that for any given , there exists such that the f…
Chi-boundedness of graphs containing no cycles with chords
Joonkyung Lee, Shoham Letzter, Alexey Pokrovskiy
We prove that the family of graphs containing no cycle with exactly -chords is -bounded, for large enough or of form with an integer. This ver…
Common graphs with arbitrary connectivity and chromatic number
Sejin Ko, Joonkyung Lee
A graph is common if the number of monochromatic copies of in a 2-edge-colouring of the complete graph is asymptotically minimised by the random colouring. We prove t…
Majority dynamics on sparse random graphs
Debsoumya Chakraborti, Jeong Han Kim, Joonkyung Lee +1
Majority dynamics on a graph is a deterministic process such that every vertex updates its -assignment according to the majority assignment on its neighbor simultaneousl…
On graph norms for complex-valued functions
Joonkyung Lee, Alexander Sidorenko
For any given graph , one may define a natural corresponding functional for real-valued functions by using homomorphism density. One may also extend this to complex-va…
On tripartite common graphs
Andrzej Grzesik, Joonkyung Lee, Bernard Lidický +1
A graph H is common if the number of monochromatic copies of H in a 2-edge-colouring of the complete graph is minimised by the random colouring. Burr and Rosta, extending a famous…
Convex graphon parameters and graph norms
Joonkyung Lee, Bjarne Schülke
Sidorenko's conjecture states that the number of copies of a bipartite graph in a graph is asymptotically minimised when is a quasirandom graph. A notorious example whe…
Two remarks on graph norms
Frederik Garbe, Jan Hladký, Joonkyung Lee
For a graph , its homomorphism density in graphs naturally extends to the space of two-variable symmetric functions in , , denoted by . One may then…
Ramsey games near the critical threshold
David Conlon, Shagnik Das, Joonkyung Lee +1
A well-known result of Rödl and Ruciński states that for any graph there exists a constant such that if , then the random graph is a.a.s.…
Odd cycles in subgraphs of sparse pseudorandom graphs
Sören Berger, Joonkyung Lee, Mathias Schacht
We answer two extremal questions about odd cycles that naturally arise in the study of sparse pseudorandom graphs. Let be an -graph, i.e., -vertex, -regular grap…
More on the extremal number of subdivisions
David Conlon, Oliver Janzer, Joonkyung Lee
Given a graph , the extremal number is the largest number of edges in an -free graph on vertices. We make progress on a number of conjectures about the…
Sidorenko's conjecture for blow-ups
David Conlon, Joonkyung Lee
A celebrated conjecture of Sidorenko and Erdős-Simonovits states that, for all bipartite graphs , quasirandom graphs contain asymptotically the minimum number of copies of t…
On the extremal number of subdivisions
David Conlon, Joonkyung Lee
One of the cornerstones of extremal graph theory is a result of Füredi, later reproved and given due prominence by Alon, Krivelevich and Sudakov, saying that if is a bipartite…
Sidorenko's conjecture for higher tree decompositions
David Conlon, Jeong Han Kim, Choongbum Lee +1
This is a companion note to our paper 'Some advances on Sidorenko's conjecture', elaborating on a remark in that paper that the approach which proves Sidorenko's conjecture for str…
On some graph densities in locally dense graphs
Joonkyung Lee
The Kohayakawa-Nagle-Rödl-Schacht conjecture roughly states that every sufficiently large locally -dense graph on vertices must contain at least $(1-o(1))d^{|E(H)|}n^{|V…
Finite reflection groups and graph norms
David Conlon, Joonkyung Lee
Given a graph on vertex set and a function , define \begin{align*} \|f\|_{H}:=\left\vert\int \prod_{ij\in E(H)}f(x_i,x_j)d…