Academic Appointments
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Professor, Mathematics
2025-26 Courses
- Modern Mathematics: Discrete Methods
MATH 62DM (Win) -
Independent Studies (3)
- Advanced Reading and Research
CS 499 (Aut, Win, Spr, Sum) - Advanced Reading and Research
CS 499P (Aut, Win, Spr, Sum) - Advanced Reading and Research
MATH 360 (Aut, Win, Spr, Sum)
- Advanced Reading and Research
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Prior Year Courses
2024-25 Courses
- Graph Theory
MATH 107 (Aut)
2023-24 Courses
- Modern Mathematics: Discrete Methods
MATH 61DM (Aut) - Topics in Combinatorics
MATH 233C (Spr)
2022-23 Courses
- Modern Mathematics: Discrete Methods
MATH 63DM (Spr) - Topics in Combinatorics
MATH 233C (Spr)
- Graph Theory
Stanford Advisees
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Doctoral Dissertation Reader (AC)
Nathan Tung -
Postdoctoral Faculty Sponsor
Tara Abrishami -
Doctoral Dissertation Advisor (AC)
Carl Schildkraut, Shengtong Zhang -
Doctoral (Program)
Anqi Li, Richard Ueltzen
All Publications
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Triangle Ramsey numbers of complete graphs
JOURNAL OF COMBINATORIAL THEORY SERIES B
2026; 176: 268-286
View details for DOI 10.1016/j.jctb.2025.08.004
View details for Web of Science ID 001595414000001
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WHEN ARE OFF-DIAGONAL HYPERGRAPH RAMSEY NUMBERS POLYNOMIAL?
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
2025
View details for DOI 10.1090/proc/17321
View details for Web of Science ID 001575355700001
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A note on directed analogues of the Sidorenko and forcing conjectures
ELECTRONIC JOURNAL OF COMBINATORICS
2025; 32 (3)
View details for DOI 10.37236/11675
View details for Web of Science ID 001567686500001
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A structure theorem for pseudosegments and its applications
JOURNAL OF COMBINATORIAL THEORY SERIES B
2025; 174: 99-132
View details for DOI 10.1016/j.jctb.2025.04.007
View details for Web of Science ID 001488778800001
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On Off-Diagonal Hypergraph Ramsey Numbers
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
2025; 2025 (11)
View details for DOI 10.1093/imrn/rnaf122
View details for Web of Science ID 001493406600001
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Induced subgraph density. II. Sparse and dense sets in cographs
EUROPEAN JOURNAL OF COMBINATORICS
2025; 124
View details for DOI 10.1016/j.ejc.2024.104075
View details for Web of Science ID 001334840800001
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Ramsey numbers of hypergraphs with a given size
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY
2025
View details for DOI 10.1017/S0305004124000409
View details for Web of Science ID 001395422200001
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The growth rate of multicolor Ramsey numbers of 3-graphs.
Research in the mathematical sciences
2024; 11 (3): 52
Abstract
The q-color Ramsey number of a k-uniform hypergraph G, denoted r(G; q), is the minimum integer N such that any coloring of the edges of the complete k-uniform hypergraph on N vertices contains a monochromatic copy of G. The study of these numbers is one of the most central topics in combinatorics. One natural question, which for triangles goes back to the work of Schur in 1916, is to determine the behavior of r(G; q) for fixed G and q tending to infinity. In this paper, we study this problem for 3-uniform hypergraphs and determine the tower height of r(G; q) as a function of q. More precisely, given a hypergraph G, we determine when r(G; q) behaves polynomially, exponentially or double exponentially in q. This answers a question of Axenovich, Gyárfás, Liu and Mubayi.
View details for DOI 10.1007/s40687-024-00463-w
View details for PubMedID 39027703
View details for PubMedCentralID PMC11252206
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Set-Coloring Ramsey Numbers and Error-Correcting Codes Near the Zero-Rate Threshold
IEEE TRANSACTIONS ON INFORMATION THEORY
2024; 70 (6): 4074-4078
View details for DOI 10.1109/TIT.2023.3327846
View details for Web of Science ID 001230181100006
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Quasiplanar graphs, string graphs, and the Erdos-Gallai problem
EUROPEAN JOURNAL OF COMBINATORICS
2024; 119
View details for DOI 10.1016/j.ejc.2023.103811
View details for Web of Science ID 001248509200001
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Ramsey numbers of sparse digraphs
ISRAEL JOURNAL OF MATHEMATICS
2024
View details for DOI 10.1007/s11856-024-2624-y
View details for Web of Science ID 001231083600007
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SET-COLORING RAMSEY NUMBERS VIA CODES
STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA
2024; 61 (1): 1-15
View details for DOI 10.1556/012.2023.04302
View details for Web of Science ID 001222784800001
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Small subsets with large sumset: Beyond the Cauchy-Davenport bound
COMBINATORICS PROBABILITY & COMPUTING
2024
View details for DOI 10.1017/S0963548324000014
View details for Web of Science ID 001166393700001
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Discrepancy of arithmetic progressions in grids
MATHEMATIKA
2024; 70 (1)
View details for DOI 10.1112/mtk.12237
View details for Web of Science ID 001135369700001
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Enumeration of Intersection Graphs of <i>x</i>-Monotone Curves
edited by Felsner, S., Klein, K.
SCHLOSS DAGSTUHL, LEIBNIZ CENTER INFORMATICS. 2024
View details for DOI 10.4230/LIPIcs.GD.2024.4
View details for Web of Science ID 001540278400002
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On random irregular subgraphs
RANDOM STRUCTURES & ALGORITHMS
2023
View details for DOI 10.1002/rsa.21204
View details for Web of Science ID 001114160800001
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On the number of edges of separated multigraphs
JOURNAL OF GRAPH THEORY
2023
View details for DOI 10.1002/jgt.23030
View details for Web of Science ID 001070119800001
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Extremal results on feedback arc sets in digraphs
RANDOM STRUCTURES & ALGORITHMS
2023
View details for DOI 10.1002/rsa.21179
View details for Web of Science ID 001050838300001
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Hypergraph Ramsey numbers of cliques versus stars
RANDOM STRUCTURES & ALGORITHMS
2023
View details for DOI 10.1002/rsa.21155
View details for Web of Science ID 000991893000001
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Three Early Problems on Size Ramsey Numbers
COMBINATORICA
2023
View details for DOI 10.1007/s00493-023-00034-7
View details for Web of Science ID 000988341300006
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Sunflowers in Set Systems of Bounded Dimension
COMBINATORICA
2023
View details for DOI 10.1007/s00493-023-00012-z
View details for Web of Science ID 000988341300005
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Off-diagonal book Ramsey numbers
COMBINATORICS PROBABILITY & COMPUTING
2023; 32 (3): 516-545
View details for DOI 10.1017/S0963548322000360
View details for Web of Science ID 001135470400008
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Threshold Ramsey multiplicity for paths and even cycles
EUROPEAN JOURNAL OF COMBINATORICS
2023; 107
View details for DOI 10.1016/j.ejc.2022.103612
View details for Web of Science ID 000860918800002
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GEOMETRIC AND O-MINIMAL LITTLEWOOD-OFFORD PROBLEMS
ANNALS OF PROBABILITY
2023; 51 (1): 101-126
View details for DOI 10.1214/22-AOP1590
View details for Web of Science ID 000894480100003
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Quasiplanar Graphs, String Graphs, and the Erdos-Gallai Problem
edited by Angelini, P., vonHanxleden, R.
SPRINGER INTERNATIONAL PUBLISHING AG. 2023: 219-231
View details for DOI 10.1007/978-3-031-22203-0_16
View details for Web of Science ID 000964584300016
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Tower-type bounds for Roth's theorem with popular differences
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY
2023; 25 (10): 3795-3831
View details for DOI 10.4171/JEMS/1271
View details for Web of Science ID 001063279500001
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Discrepancy in modular arithmetic progressions
COMPOSITIO MATHEMATICA
2022; 158 (11): 2082-2108
View details for DOI 10.1112/S0010437X22007758
View details for Web of Science ID 000892888900001
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The upper logarithmic density of monochromatic subset sums
MATHEMATIKA
2022; 68 (4): 1292-1301
View details for DOI 10.1112/mtk.12167
View details for Web of Science ID 000865718800001
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Minimum degree and the graph removal lemma
JOURNAL OF GRAPH THEORY
2022
View details for DOI 10.1002/jgt.22891
View details for Web of Science ID 000859560300001
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Making an H $H$-free graph k $k$-colorable
JOURNAL OF GRAPH THEORY
2022
View details for DOI 10.1002/jgt.22868
View details for Web of Science ID 000840714300001
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THRESHOLD RAMSEY MULTIPLICITY FOR ODD CYCLES
REVISTA DE LA UNION MATEMATICA ARGENTINA
2022; 64 (1): 49-68
View details for DOI 10.33044/revuma.2874
View details for Web of Science ID 000874761200004
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Multicolor list Ramsey numbers grow exponentially
JOURNAL OF GRAPH THEORY
2022
View details for DOI 10.1002/jgt.22832
View details for Web of Science ID 000778509000001
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RAMSEY NUMBERS OF BOOKS AND QUASIRANDOMNESS
COMBINATORICA
2022
View details for DOI 10.1007/s00493-021-4409-9
View details for Web of Science ID 000767090700001
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INDUCED ARITHMETIC REMOVAL: COMPLEXITY 1 PATTERNS OVER FINITE FIELDS
ISRAEL JOURNAL OF MATHEMATICS
2022
View details for DOI 10.1007/s11856-022-2290-x
View details for Web of Science ID 000765687500003
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Removal lemmas and approximate homomorphisms
COMBINATORICS PROBABILITY & COMPUTING
2022
View details for DOI 10.1017/S0963548321000572
View details for Web of Science ID 000746271200001
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Which graphs can be counted in C-4-free graphs?
PURE AND APPLIED MATHEMATICS QUARTERLY
2022; 18 (6): 2413-2432
View details for Web of Science ID 000973130500005
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COMMON AND SIDORENKO LINEAR EQUATIONS
QUARTERLY JOURNAL OF MATHEMATICS
2021; 72 (4): 1223-1234
View details for DOI 10.1093/qmath/haaa068
View details for Web of Science ID 000733393600004
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Bounded VC-Dimension Implies the Schur-Erdos Conjecture
COMBINATORICA
2021
View details for DOI 10.1007/s00493-021-4530-9
View details for Web of Science ID 000721431700001
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Powers of paths in tournaments
COMBINATORICS PROBABILITY & COMPUTING
2021; 30 (6): 894-898
View details for DOI 10.1017/S0963548321000067
View details for Web of Science ID 000753894400003
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The regularity method for graphs with few 4-cycles
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES
2021
View details for DOI 10.1112/jlms.12500
View details for Web of Science ID 000701861200001
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Combinatorial anti-concentration inequalities, with applications
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY
2021; 171 (2): 227-248
View details for DOI 10.1017/S0305004120000183
View details for Web of Science ID 000684260600001
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Clique minors in graphs with a forbidden subgraph
RANDOM STRUCTURES & ALGORITHMS
2021
View details for DOI 10.1002/rsa.21038
View details for Web of Science ID 000685424700001
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ANTI-CONCENTRATION FOR SUBGRAPH COUNTS IN RANDOM GRAPHS
ANNALS OF PROBABILITY
2021; 49 (3): 1515-1553
View details for DOI 10.1214/20-AOP1490
View details for Web of Science ID 000647283800015
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On the inducibility problem for random Cayley graphs of abelian groups with a few deleted vertices
RANDOM STRUCTURES & ALGORITHMS
2021
View details for DOI 10.1002/rsa.21010
View details for Web of Science ID 000642636200001
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Popular Progression Differences in Vector Spaces
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
2021; 2021 (7): 5261-5289
View details for DOI 10.1093/imrn/rny240
View details for Web of Science ID 000648945900015
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Independent sets in hypergraphs with a forbidden link
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY
2021
View details for DOI 10.1112/plms.12400
View details for Web of Science ID 000629792600001
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Acyclic subgraphs of tournaments with high chromatic number
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY
2021
View details for DOI 10.1112/blms.12446
View details for Web of Science ID 000604749200001
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Extremal and Ramsey results on graph blowups
JOURNAL OF COMBINATORICS
2021; 12 (1): 1–15
View details for Web of Science ID 000605448000001
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TOMESCU'S GRAPH COLORING CONJECTURE FOR l-CONNECTED GRAPHS
SIAM JOURNAL ON DISCRETE MATHEMATICS
2021; 35 (2): 1478-1502
View details for DOI 10.1137/19M1306646
View details for Web of Science ID 000674142200042
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ON THE NUMBER OF CLIQUES IN GRAPHS WITH A FORBIDDEN SUBDIVISION OR IMMERSION
SIAM JOURNAL ON DISCRETE MATHEMATICS
2021; 34 (4): 2556-2582
View details for DOI 10.1137/18M1206126
View details for Web of Science ID 000729692100001
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A NOTE ON THE ERDOS DISTINCT SUBSET SUMS PROBLEM
SIAM JOURNAL ON DISCRETE MATHEMATICS
2021; 35 (1): 322–24
View details for DOI 10.1137/20M1385883
View details for Web of Science ID 000636039400017
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Sets without k-term progressions can have many shorter progressions
RANDOM STRUCTURES & ALGORITHMS
2020
View details for DOI 10.1002/rsa.20984
View details for Web of Science ID 000598748500001
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On edge-ordered Ramsey numbers
RANDOM STRUCTURES & ALGORITHMS
2020
View details for DOI 10.1002/rsa.20954
View details for Web of Science ID 000564585100001
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Short proofs of some extremal results III
RANDOM STRUCTURES & ALGORITHMS
2020
View details for DOI 10.1002/rsa.20953
View details for Web of Science ID 000563774100001
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The Schur-Erdos problem for sesmi-algebraic colorings
ISRAEL JOURNAL OF MATHEMATICS
2020
View details for DOI 10.1007/s11856-020-2042-8
View details for Web of Science ID 000553232300004
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Ramsey, Paper, Scissors
RANDOM STRUCTURES & ALGORITHMS
2020
View details for DOI 10.1002/rsa.20950
View details for Web of Science ID 000550520100001
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Triforce and corners
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY
2020; 169 (1): 209–23
View details for DOI 10.1017/S0305004119000173
View details for Web of Science ID 000545996900009
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Towards the linear arboricity conjecture
COMPUTATIONAL STATISTICS & DATA ANALYSIS
2020; 145: 56–79
View details for DOI 10.1016/j.jctb.2019.08.009
View details for Web of Science ID 000521518000004
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Pure pairs. III. Sparse graphs with no polynomial-sized anticomplete pairs
JOURNAL OF GRAPH THEORY
2020
View details for DOI 10.1002/jgt.22556
View details for Web of Science ID 000562040000001
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A short proof of the canonical polynomial van der Waerden theorem
COMPTES RENDUS MATHEMATIQUE
2020; 358 (8): 957–59
View details for DOI 10.5802/crmath.101
View details for Web of Science ID 000596067600010
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On Ramsey numbers of hedgehogs
COMBINATORICS PROBABILITY & COMPUTING
2020; 29 (1): 101–12
View details for DOI 10.1017/S0963548319000312
View details for Web of Science ID 000578255000006
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BOOKS VERSUS TRIANGLES AT THE EXTREMAL DENSITY
SIAM JOURNAL ON DISCRETE MATHEMATICS
2020; 34 (1): 385–98
View details for DOI 10.1137/19M1261766
View details for Web of Science ID 000546886700019
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FINDING CLIQUES IN SOCIAL NETWORKS: A NEW DISTRIBUTION-FREE MODEL
SIAM JOURNAL ON COMPUTING
2020; 49 (2): 448–64
View details for DOI 10.1137/18M1210459
View details for Web of Science ID 000546873800007
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Popular Progression Differences in Vector Spaces II
DISCRETE ANALYSIS
2019
View details for DOI 10.19086/da.11002
View details for Web of Science ID 000508366200001
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TOWER-TYPE BOUNDS FOR UNAVOIDABLE PATTERNS IN WORDS
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
2019; 372 (9): 6213–29
View details for DOI 10.1090/tran/7751
View details for Web of Science ID 000514301800006
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Towards Erds-Hajnal for Graphs with No 5-Hole
COMBINATORICA
2019
View details for DOI 10.1007/s00493-019-3957-8
View details for Web of Science ID 000488910800002
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A fast new algorithm for weak graph regularity
COMBINATORICS PROBABILITY & COMPUTING
2019; 28 (5): 777–90
View details for DOI 10.1017/S0963548319000075
View details for Web of Science ID 000500255000009
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HYPERGRAPH CUTS ABOVE THE AVERAGE
ISRAEL JOURNAL OF MATHEMATICS
2019; 233 (1): 67–111
View details for DOI 10.1007/s11856-019-1897-z
View details for Web of Science ID 000489755900004
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Approximating the rectilinear crossing number
COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS
2019; 81: 45–53
View details for DOI 10.1016/j.comgeo.2019.04.003
View details for Web of Science ID 000468713600005
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Erds-Hajnal Conjecture for Graphs with Bounded VC-Dimension
SPRINGER. 2019: 809–29
View details for DOI 10.1007/s00454-018-0046-5
View details for Web of Science ID 000466130000006
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The removal lemma for tournaments
JOURNAL OF COMBINATORIAL THEORY SERIES B
2019; 136: 110–34
View details for DOI 10.1016/j.jctb.2018.10.001
View details for Web of Science ID 000462695000006
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A proof of Tomescu's graph coloring conjecture
JOURNAL OF COMBINATORIAL THEORY SERIES B
2019; 136: 204–21
View details for DOI 10.1016/j.jctb.2018.10.005
View details for Web of Science ID 000462695000011
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Efficient Arithmetic Regularity and Removal Lemmas for Induced Bipartite Patterns
DISCRETE ANALYSIS
2019
View details for DOI 10.19086/da.7757
View details for Web of Science ID 000467650900001
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Lines in Euclidean Ramsey Theory
DISCRETE & COMPUTATIONAL GEOMETRY
2019; 61 (1): 218–25
View details for DOI 10.1007/s00454-018-9980-5
View details for Web of Science ID 000463139600012
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Ramsey-Turan numbers for semi-algebraic graphs
ELECTRONIC JOURNAL OF COMBINATORICS
2018; 25 (4)
View details for Web of Science ID 000456788300016
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A polynomial bound for the arithmetic k-cycle removal lemma in vector spaces
JOURNAL OF COMBINATORIAL THEORY SERIES A
2018; 160: 186–201
View details for DOI 10.1016/j.jcta.2018.06.004
View details for Web of Science ID 000445054200008
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On Regularity Lemmas and their Algorithmic Applications (vol 26, pg 481, 2017)
COMBINATORICS PROBABILITY & COMPUTING
2018; 27 (5): 851–52
View details for DOI 10.1017/S0963548318000111
View details for Web of Science ID 000448028700009
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Fast Property Testing and Metrics for Permutations
CAMBRIDGE UNIV PRESS. 2018: 539–79
View details for DOI 10.1017/S096354831800024X
View details for Web of Science ID 000435718200008
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Hereditary quasirandomness without regularity
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY
2018; 164 (3): 385–99
View details for DOI 10.1017/S0305004116001055
View details for Web of Science ID 000429689600001
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Erdos-Ginzburg-Ziv constants by avoiding three-term arithmetic progressions
ELECTRONIC JOURNAL OF COMBINATORICS
2018; 25 (2)
View details for Web of Science ID 000432169900007
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More Distinct Distances Under Local Conditions
COMBINATORICA
2018; 38 (2): 501–9
View details for DOI 10.1007/s00493-016-3637-x
View details for Web of Science ID 000432109400009
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A tight lower bound for Szemer,di's regularity lemma
COMBINATORICA
2017; 37 (5): 911–51
View details for DOI 10.1007/s00493-016-3274-4
View details for Web of Science ID 000418056000006
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On graphs decomposable into induced matchings of linear sizes
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY
2017; 49 (1): 45-57
View details for DOI 10.1112/blms.12005
View details for Web of Science ID 000398892300005
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Ordered Ramsey numbers
JOURNAL OF COMBINATORIAL THEORY SERIES B
2017; 122: 353-383
View details for DOI 10.1016/j.jctb.2016.06.007
View details for Web of Science ID 000389788300016
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Permutation Property Testing under Different Metrics with Low Query Complexity
ASSOC COMPUTING MACHINERY. 2017: 1618–37
View details for Web of Science ID 000426965800107
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A tight bound for Green's arithmetic triangle removal lemma in vector spaces
ASSOC COMPUTING MACHINERY. 2017: 1612–17
View details for Web of Science ID 000426965800106
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Short proofs of some extremal results II
JOURNAL OF COMBINATORIAL THEORY SERIES B
2016; 121: 173-196
View details for DOI 10.1016/j.jctb.2016.03.005
View details for Web of Science ID 000388249800006
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On the minimum degree of minimal Ramsey graphs for multiple colours
JOURNAL OF COMBINATORIAL THEORY SERIES B
2016; 120: 64-82
View details for DOI 10.1016/j.jctb.2016.03.006
View details for Web of Science ID 000377833100004
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A POLYNOMIAL REGULARITY LEMMA FOR SEMIALGEBRAIC HYPERGRAPHS AND ITS APPLICATIONS IN GEOMETRY AND PROPERTY TESTING
SIAM JOURNAL ON COMPUTING
2016; 45 (6): 2199-2223
View details for DOI 10.1137/15M1007355
View details for Web of Science ID 000391838800008
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A SHORT PROOF OF THE MULTIDIMENSIONAL SZEMEREDI THEOREM IN THE PRIMES
AMERICAN JOURNAL OF MATHEMATICS
2015; 137 (4): 1139-1145
View details for DOI 10.1353/ajm.2015.0028
View details for Web of Science ID 000358227900008