COMBINATORICA is an international journal of

**the Bolyai Mathematical Society, Hungary**,

published jointly by

the Bolyai Mathematical Society and Springer.

COMBINATORICA publishes research papers in a variety of areas of *combinatorics and the theory of computing*, with particular emphasis on *general techniques and unifying principles*.

Coverage in COMBINATORICA includes:

- combinatorial structures (graphs, matroids, hypergraphs, designs, permutation groups);
- combinatorial optimization;
- combinatorial aspects of geometry and number theory;
- algorithms in combinatorics and related fields;
- computational complexity theory;
- randomization and explicit construction in combinatorics and algorithms.

Six issues appear each year. A total of 30-40 papers are accepted for publication out of roughly 300 submissions per year.

**Imre Bárány**, Rényi Institute of Mathematics, Budapest

**József Solymosi**, University of British Columbia

**László Babai**, University of Chicago

**László Lovász**, ELTE Eötvös University, Budapest

**Lilla Tóthmérész**, ELTE Eötvös University, Budapest

**Viktor Harangi**, Rényi Institute of Mathematics, Budapest

**Gyula O.H. Katona**, Rényi Institute of Mathematics, Budapest

**Miklós Simonovits**, Rényi Institute of Mathematics, Budapest

** Vera T. Sós ** 1930—2023

**Endre Szemerédi**, Rényi Institute of Mathematics, Budapest

**Miklós Abért**, Rényi Institute of Mathematics, Budapest

**Noga Alon**, Tel Aviv University & Princeton University

**József Balogh**, University of Illinois

**Anders Björner**, Royal Institute of Technology (KTH), Stockholm

**Béla Bollobás**, University of Cambridge & The University of Memphis

**Maria Chudnovsky**, Princeton University

**András Frank**, ELTE Eötvös University, Budapest

**Peter Frankl**, Rényi Institute of Mathematics, Budapest

**Zoltán Füredi**, Rényi Institute of Mathematics, Budapest

**Péter Komjáth**, ELTE Eötvös University, Budapest

**Nathan Linial**, The Hebrew University of Jerusalem

**Jaroslav Nešetřil**, Charles University, Prague

**János Pach**, Rényi Institute of Mathematics, Budapest & EPFL, Lausanne

**Alexander A. Razborov**, University of Chicago & Steklov Math. Inst., Moscow

**Vojtěch Rödl**, Emory University, Atlanta

**Imre Z. Ruzsa**, Rényi Institute of Mathematics, Budapest

**Lisa Sauermann**, MIT

**Alexander Schrijver**, CWI Amsterdam & University of Amsterdam

**Alexander Scott**, University of Oxford

**Paul D. Seymour**, Princeton University

**Benny Sudakov**, ETH, Zürich

**Gábor Tardos**, Rényi Institute of Mathematics, Budapest

**Van H. Vu**, Yale University

**Avi Wigderson**, Institute for Advanced Study, Princeton

Papers can be submitted to COMBINATORICA
via EditFlow.

Please **read the instructions below** before submission.

*Submission.*Manuscripts should be submitted via the editorial system EditFlow. Please use the following link: https://ef.msp.org/submit/combinatorica*Length.*The length of the paper should not exceed 30 pages (in 11-point LaTeX format on US letter-size paper with 1-inch margins). Authors of longer papers are advised to submit a 30-page version to COMBINATORICA with a link to a full version on arXiv.*Notes.*Short notes are welcome and processed in an expedited fashion.*Form of the manuscript.*The manuscript should contain a brief abstract. In a paper divided into sections, it is desirable to number theorems, lemmas, definitions, corollaries, examples, etc. consecutively using double Arabic numerals. (E.g., Section 3 may start with Definition 3.1 followed by Remark 3.2 and Theorem 3.3).*Style.*Clarity of the presentation is paramount. The results should be made accessible to the non-specialist reader. Authors should give clear motivation, background, and exact references.*Final version.*If the paper is accepted, the following should be submitted.- The final version of the paper in TeX/LaTeX format. It is best to avoid using complicated macros or non-standard packages and fonts as they tend to be in conflict with the journal format. Furthermore, it significantly simplifies the typesetting process if unused packages and definitions are deleted by the author. In general, a plain "vanilla" version is the least prone to errors when adapting it to the journal format.
- Each figure in a separate file (in a vector graphic format that can handle embedded fonts such as EPS or vector PDF). Note that while the online version is published in color, the print version is converted to grayscale. Ensure that the figure can still be understood even when it is printed in grayscale. For example, avoid referring to colors in the text.
- Affiliation and e-mail address for each author.
- Abbreviated title (at most 35 characters), to be used as the running head.
- Mathematics Subject Classification codes (primary and secondary).

*Reprints.*50 Reprints are provided free of charge upon request. Additional reprints may be ordered.

Papers waiting to be assigned to an issue: Online First articles.

Marcin Briański, James Davies, Bartosz Walczak

Separating Polynomial Chi-Boundedness from Chi-Boundedness

Pages 1-8 | DOI:10.1007/s00493-023-00054-3

Konstantin Tikhomirov

On Bounded Degree Graphs with Large Size-Ramsey Numbers

Pages 9-14 | DOI:10.1007/s00493-023-00056-1

P. Frankl

On the Maximum of the Sum of the Sizes of Non-trivial Cross-Intersecting Families

Pages 15-35 | DOI:10.1007/s00493-023-00060-5

António Girão, Freddie Illingworth, Emil Powierski, Michael Savery, Alex Scott, Youri Tamitegama , Jane Tan

Induced Subgraphs of Induced Subgraphs of Large Chromatic Number

Pages 37-62 | DOI:10.1007/s00493-023-00061-4

Arnau Padrol, Eva Philippe

Sweeps, Polytopes, Oriented Matroids, and Allowable Graphs of Permutations

Pages 63-123 | DOI:10.1007/s00493-023-00062-3

Daniel W. Cranston, Reem Mahmoud

Kempe Equivalent List Colorings

Pages 125-153 | DOI:10.1007/s00493-023-00063-2

Sam Mansfield, Jonathan Passant

A Structural Theorem for Sets with Few Triangles

Pages 155-178 | DOI:10.1007/s00493-023-00066-z

Yuxuan Li, Binzhou Xia, Sanming Zhou , Wenying Zhu

A Solution to Babai’s Problems on Digraphs with Non-diagonalizable Adjacency Matrix

Pages 179-203 | DOI:10.1007/s00493-023-00068-x

Torsten Mütze

A Book Proof of the Middle Levels Theorem

Pages 205-208 | DOI:10.1007/s00493-023-00070-3

Florian Lehner

Universal Planar Graphs for the Topological Minor Relation

Pages 209-230 | DOI:10.1007/s00493-023-00073-0

József Balogh, Ce Chen, Kevin Hendrey, Ben Lund, Haoran Luo, Casey Tompkins, Tuan Tran

Maximal 3-Wise Intersecting Families

Pages 1045-1066 | DOI:10.1007/s00493-023-00046-3

Claude Tardif

The Chromatic Number of the Product of 5-Chromatic Graphs can be 4

Pages 1067-1073 | DOI:10.1007/s00493-023-00047-2

Marcelo Sales, Bjarne Schülke

A Local Version of Katona’s Intersecting Shadow Theorem

Pages 1075-1080 | DOI:10.1007/s00493-023-00048-1

Denys Bulavka, Martin Tancer, Mykhaylo Tyomkyn

Weak Saturation of Multipartite Hypergraphs

Pages 1081-1102 | DOI:10.1007/s00493-023-00049-0

Daniel McGinnis

A Necessary and Sufficient Condition for (2d-2)-Transversals in R^2d

Pages 1103-1109 | DOI:10.1007/s00493-023-00050-7

Gaurav Kucheriya, Gábor Tardos

A Characterization of Edge-Ordered Graphs with Almost Linear Extremal Functions

Pages 1111-1123 | DOI:10.1007/s00493-023-00052-5

Jun Gao, Hong Liu, Zixiang Xu

Stability Through Non-Shadows

Pages 1125-1137 | DOI:10.1007/s00493-023-00053-4

Andrew Granville, George Shakan, Aled Walker

Effective Results on the Size and Structure of Sumsets

Pages 1139-1178 | DOI:10.1007/s00493-023-00055-2

David J. Grynkiewicz

A Generalization of the Chevalley–Warning and Ax–Katz Theorems with a View Towards Combinatorial Number Theory

Pages 1179-1213 | DOI:10.1007/s00493-023-00057-0

Sebastian Mies, Benjamin Moore

The Strong Nine Dragon Tree Conjecture is True for d≤k+1

Pages 1215-1239 | DOI:10.1007/s00493-023-00058-z

Alex Scott, Paul Seymour, Sophie Spirkl

Polynomial Bounds for Chromatic Number. IV: A Near-polynomial Bound for Excluding the Five-vertex Path

Pages 845-852 | DOI:10.1007/s00493-023-00015-w

He Guo, Kalen Patton, Lutz Warnke

Prague Dimension of Random Graphs

Pages 853-884 | DOI:10.1007/s00493-023-00016-9

Bingyu Luan, Yantao Tang, Guanghui Wang, Donglei Yang

Balanced Subdivisions of Cliques in Graphs

Pages 885-907 | DOI:10.1007/s00493-023-00039-2

Davi Castro-Silva, Fernando Mário de Oliveira Filho, Lucas Slot, Frank Vallentin

A Recursive Theta Body for Hypergraphs

Pages 909-938 | DOI:10.1007/s00493-023-00040-9

Balázs Keszegh, Dömötör Pálvölgyi

The Number of Tangencies Between Two Families of Curves

Pages 939-952 | DOI:10.1007/s00493-023-00041-8

Joshua Hinman

A Positive Answer to Bárány’s Question on Face Numbers of Polytopes

Pages 953-962 | DOI:10.1007/s00493-023-00042-7

Donggyu Kim, Duksang Lee, Sang-il Oum

Γ-Graphic Delta-Matroids and Their Applications

Pages 963-983 | DOI:10.1007/s00493-023-00043-6

Minki Kim, Alan Lew

Leray Numbers of Tolerance Complexes

Pages 985-1006 | DOI:10.1007/s00493-023-00044-5

Patrick Schnider

Enclosing Depth and Other Depth Measures

Pages 1007-1029 | DOI:10.1007/s00493-023-00045-4

Guyslain Naves

Integer Multiflows in Acyclic Planar Digraphs

Pages 1031-1043 | DOI:10.1007/s00493-023-00065-0

Lubotzky, A.; Phillips, R.; Sarnak, P.

Ramanujan graphs

Volume 8 (1988), Issue 3, 261–277

Karmarkar, N.

A new polynomial-time algorithm for linear programming

Volume 4 (1984), Issue 4, 373–395

Grötschel, M.; Lovász, L.; Schrijver, A.

The ellipsoid method and its consequences in combinatorial optimization

Volume 1 (1981), Issue 2, 169–197

Alon, N.

Eigenvalues and expanders

Volume 6 (1986), Issue 2, 83–96

Linial, Nathan; London, Eran; Rabinovich, Yuri

The geometry of graphs and some of its algorithmic applications

Volume 15 (1995), Issue 2, 215–245

Alon, N.; Tarsi, M.

Colorings and orientations of graphs

Volume 12 (1992), Issue 2, 125–134

Chung, F. R. K.; Graham, R. L.; Wilson, R. M.

Quasi-random graphs

Volume 9 (1989), Issue 4, 345–362

Szemerédi, Endre; Trotter, William T., Jr.

Extremal problems in discrete geometry

Volume 3 (1983), Issue 3-4, 381–392

de Fraysseix, H.; Pach, J.; Pollack, R.

How to draw a planar graph on a grid

Volume 10 (1990), Issue 1, 41–51

Frankl, P.; Wilson, R. M.

Intersection theorems with geometric consequences

Volume 1 (1981), Issue 4, 357–368

Godsil, C. D.

On the full automorphism group of a graph

Volume 1 (1981), Issue 3, 243–256

Füredi, Z.; Komlós, J.

The eigenvalues of random symmetric matrices

Volume 1 (1981), Issue 3, 233–241

Frieze, Alan; Kannan, Ravi

Quick approximation to matrices and applications

Volume 19 (1999), Issue 2, 175–220

Komlós, János; Sárközy, Gábor N.; Szemerédi, Endre

Blow-up lemma

Volume 17 (1997), Issue 1, 109–123

Wilson, Richard M.

The exact bound in the Erdős-Ko-Rado theorem

Volume 4 (1984), Issue 2-3, 247–257

Pach, János; Tóth, Géza

Graphs drawn with few crossings per edge

Volume 17 (1997), Issue 3, 427–439

Babai, L.

On Lovász' lattice reduction and the nearest lattice point problem

Volume 6 (1986), Issue 1, 1–13

Mulmuley, Ketan; Vazirani, Umesh V.; Vazirani, Vijay V.

Matching is as easy as matrix inversion

Volume 7 (1987), Issue 1, 105–113

Raghavan, P.; Thompson, C. D.

Randomized rounding: a technique for provably good algorithms and algorithmic proofs

Volume 7 (1987), Issue 4, 365–374

Robertson, Neil; Seymour, Paul; Thomas, Robin

Hadwiger's conjecture for K6-free graphs

Volume 13 (1993), Issue 3, 279–361

Jain, Kamal

A factor 2 approximation algorithm for the generalized Steiner network problem

Volume 21 (2001), Issue 1, 39–60

Bollobás, Béla; Riordan, Oliver

The diameter of a scale-free random graph

Volume 24 (2004), Issue 1, 5–34

Chudnovsky, Maria; Cornuéjols, Gérard; Liu, Xinming; Seymour, Paul; Vušković, Kristina

Recognizing Berge graphs

Volume 25 (2005), Issue 2, 143–186

Alon, Noga; Fischer, Eldar; Krivelevich, Michael; Szegedy, Mario

Efficient testing of large graphs

Volume 20 (2000), Issue 4, 451–476

Tao, Terence

Product set estimates for non-commutative groups

Volume 28 (2008), Issue 5, 547–594

Linial, Nathan; Meshulam, Roy

Homological connectivity of random 2-complexes

Volume 26 (2006), Issue 4, 475–487

Kim, Jeong Han; Vu, Van H.

Concentration of multivariate polynomials and its applications

Volume 20 (2000), Issue 3, 417–434

Thomassé, Stéphan; Yeo, Anders

Total domination of graphs and small transversals of hypergraphs

Volume 27 (2007), Issue 4, 473–487

Goldreich, Oded; Goldwasser, Shafi; Lehman, Eric; Ron, Dana; Samorodnitsky, Alex

Testing monotonicity

Volume 20 (2000), Issue 3, 301–337

Kühn, Daniela; Osthus, Deryk

The minimum degree threshold for perfect graph packings

Volume 29 (2009), Issue 1, 65–107

Sebő, András; Vygen, Jens

Shorter tours by nicer ears: 7/5-approximation for the graph-TSP, 3/2 for the path version, and 4/3 for two-edge-connected subgraphs

Volume 34 (2014), Issue 5, 597–629

Petridis, Giorgis

New proofs of Plünnecke-type estimates for product sets in groups

Volume 32 (2012), Issue 6, 721–733

Tóth, Csaba D.

The Szemerédi-Trotter theorem in the complex plane

Volume 35 (2015), Issue 1, 95–126

Ceballos, Cesar; Santos, Francisco; Ziegler, Günter M.

Many non-equivalent realizations of the associahedron

Volume 35 (2015), Issue 5, 513–551

Dujmović, Vida; Joret, Gwenaël; Kozik, Jakub; Wood, David R.

Nonrepetitive colouring via entropy compression

Volume 36 (2016), Issue 6, 661–686

Chudnovsky, Maria; Seymour, Paul

The three-in-a-tree problem

Volume 30 (2010), Issue 4, 387–417

Füredi, Zoltán; Jiang, Tao; Seiver, Robert

Exact solution of the hypergraph Turán problem for k-uniform linear paths

Volume 34 (2014), Issue 3, 299–322

Raigorodskii, A. M.

On the chromatic numbers of spheres in Rn

Volume 32 (2012), Issue 1, 111–123

Cilleruelo, Javier

Combinatorial problems in finite fields and Sidon sets

Volume 32 (2012), Issue 5, 497–511

Devos, Matt; Dvořák, Zdeněk; Fox, Jacob; McDonald, Jessica; Mohar, Bojan; Scheide, Diego

A minimum degree condition forcing complete graph immersion

Volume 34 (2014), Issue 3, 279–298

Rudnev, Misha

On the number of incidences between points and planes in three dimensions

Volume 38 (2018), Issue 1, 219–254

If you have any question, please do not hesitate to contact us at

Note that papers can **no longer** be submitted via e-mail:

submission information.

Postal address:

*COMBINATORICA
Rényi Institute of Mathematics
Reáltanoda u. 13-15.
H-1053, Budapest, Hungary*

For information on journal subscription,

please visit
the Springer website.

For orders within Hungary, please contact the

Bolyai Mathematical Society.