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

**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**, Rényi Institute of Mathematics, Budapest

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

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

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

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

**Aart Blokhuis**, Eindhoven University of Technology

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

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

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

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

**W. Timothy Gowers**, University of Cambridge

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

**Daniela Kühn**, University of Birmingham

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

**Dániel Marx**, Max Planck Institute for Informatics

**Jaroslav Nešetřil**, Charles University, Prague

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

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

**Vojtěch Rödl**, Emory University, Atlanta

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

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

**Paul D. Seymour**, Princeton University

**Benny Sudakov**, ETH, Zürich

**Tamás Szőnyi**, ELTE Eötvös University, Budapest

**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.

The papers below are accepted for publication in COMBINATORICA and will appear in upcoming issues. Some have already been published electronically and can be accessed on the Springer website: Online First articles.

Dana Bartosova, Jordi Lopez-Abad, Martino Lupini, Brice Mbombo

**The Ramsey properties for Grassmannians over R, C**

Daniel Kráľ, Jonathan A. Noel, Sergey Norin, Jan Volec, Fan Wei

**Non-bipartite k-common graphs**

Luke Postle, Evelyne Smith-Roberge

**On The Density of C_7-Critical Graphs**

Jan Grebik, Israel Rocha

**Fractional isomorphism of graphons**

François Hennecart, Gyan Prakash, E. Pramod

**On thin sum-product bases**

Tomasz Łuczak, Joanna Polcyn, Christian Reiher

**On the Ramsey-Turán density of triangles**

Sergey Norin, Zi-Xia Song

**A new upper bound on the chromatic number of graphs with no odd K_t minor**

Dávid Matolcsi, Imre Ruzsa, George Shakan, Dmitrii Zhelezov

**An Analytic Approach to the Cardinalities of Sumsets**

David Conlon, Jacob Fox, Yuval Wigderson

**Ramsey numbers of books and quasirandomness**

Zhicong Lin, Dongsu Kim

**A combinatorial bijection on k-noncrossing partition**

Dhruv Mubayi, Xizhi Liu

**A hypergraph Turán problem with no stability**

Peter Ayre, Amin Coja-Oghlan, Catherine Greenhill

**Lower bounds on the chromatic number of random graphs**

Brandon Hanson, Oliver Roche-Newton, Misha Rudnev

**Higher convexity and iterated sum sets**

Vida Dujmović, David Eppstein, Robert Hickingbotham, Pat Morin, David R. Wood

**Stack-Number is not Bounded by Queue-Number**

Tony Huynh, Gwenaël Joret, Piotr Micek, Michał Seweryn, Paul Joseph Wollan

**Excluding a ladder**

Sergey Avvakumov, Karim Alexander Adiprasito, Roman Karasev

**A subexponential size triangulation of RP^n**

Arnold Neumaier, Safet Penjić

**On bounding the diameter of a distance-regular graph**

Pavel Pudlak, Vojtěch Rödl

**Extractors for small zero-fixing sources**

Jana Cslovjecsek, Romanos Diogenes Malikiosis, Márton Naszódi, Matthias Schymura

**Computing the covering radius of a polytope with an application to lonely runners**

Felix Joos, Stefan Ehard

**A short proof of the blow-up lemma for approximate decompositions**

Sean Eberhard

**The characteristic polynomial of a random matrix**

Martin Balko, David Chodounský, Jan Hubička, Matěj Konečný, Lluís Vena

**Big Ramsey degrees of 3-uniform hypergraphs are finite**

Drago Bokal, Zdenek Dvorak, Petr Hlineny, Jesus Leanos, Bojan Mohar, Tilo Wiedera

**Bounded degree conjecture holds precisely for c-crossing-critical graphs with c<=12**

Maxime Fortier Bourque, Bram Petri

**Kissing numbers of regular graphs**

Bodo Lass

**Calculating the Euler characteristic of the moduli space of curves**

Tsz Ho Chan, Jared Lichtman, Carl Pomerance

**On the critical exponent for k-primitive sets**

Gábor Kun

**On Gardner's conjecture**

Daniele Bartoli, Giacomo Micheli

**Algebraic constructions of complete m-arcs**

Jeff Kahn, Jinyoung Park

**The number of maximal independent sets in the Hamming cube**

Yoichi Iwata, Yutaro Yamaguchi

**Finding a Shortest Non-zero Path in Group-Labeled Graphs**

Ronen Eldan

**Second-order bounds on correlations between increasing families**

Tomáš Masařík, Irene Muzi, Marcin Pilipczuk, Paweł Rzążewski, Manuel Sorge

**Packing Directed Cycles Quarter- and Half-Integrally**

Abhishek Methuku, István Tomon

**Bipartite Turán problems for ordered graphs**

Kenta Ozeki

**Kempe equivalence classes of cubic graphs embedded on the projective plane**

Lior Gishboliner, Raphael Steiner, Tibor Szabó

**Oriented cycles in digraphs of large outdegree**

James Davies

**Vertex-minor-closed classes are $\chi$-bounded**

Hadi Kharaghani, Thomas Pender, Sho Suda

**A family of balanced generalized weighing matrices**

Claude Tardif

**The chromatic number of the product of 14-chromatic graphs can be 13**

Tamás Kálmán, Seunghun Lee, Lilla Tóthmérész

**The sandpile group of a trinity and a canonical definition for the planar Bernardi action**

Gábor Elek, Gábor Tardos

**Convergence and limits of finite trees**

Ron Aharoni, Eli Berger, Joseph Briggs, Erel Segal-Halevi, Shira Zerbib

**Fractionally balanced hypergraphs and rainbow KKM theorems**

Hong Liu, Péter Pál Pach, Csaba Sándor

**Polynomial Schur's theorem**

Jakub Przybyło

**The 1-2-3 Conjecture holds for graphs with large enough minimum degree**

Chao Shi, Péter Frankl, Jianguo Qian

**On non-empty cross-intersecting families**

Gábor Damásdi, Dömötör Pálvölgyi

**Realizing an 𝑚-uniform four-chromatic hypergraph with disks**

Vojtěch Kaluža, Martin Tancer

**Even maps, the Colin de Verdière number and representations of graphs**

Nóra Frankl, Andrey Kupavskii

**Almost sharp bounds on the number of discrete chains in the plane**

Swee Hong Chan, Igor Pak, Greta Panova

**Log-concavity in planar random walks**

Daniel Di Benedetto, József Solymosi, Ethan P. White

On the Directions Determined by a Cartesian Product in an Affine Galois Plane

Pages 755-763 | DOI:10.1007/s00493-020-4516-z

Jakub Byszewski, Jakub Konieczny, Elżbieta Krawczyk

Substitutive Systems and a Finitary Version of Cobham’s Theorem

Pages 765-801 | DOI:10.1007/s00493-020-4311-x

Jacob Fox, János Pach, Andrew Suk

Bounded VC-Dimension Implies the Schur-Erdős Conjecture

Pages 803-813 | DOI:10.1007/s00493-021-4530-9

António Girão, Kamil Popielarz, Richard Snyder

(2K + 1)-Connected Tournaments with Large Minimum Out-Degree are K-Linked

Pages 815-837 | DOI:10.1007/s00493-021-4374-3

Gary R. W. Greaves, Jeven Syatriadi, Pavlo Yatsyna

Equiangular Lines in Low Dimensional Euclidean Spaces

Pages 839-872 | DOI:10.1007/s00493-020-4523-0

Péter Vrana

Probabilistic Refinement of the Asymptotic Spectrum of Graphs

Pages 873-904 | DOI:10.1007/s00493-020-4324-5

Bence Csajbók, Zsuzsa Weiner

Generalizing Korchmáros—Mazzocca Arcs

Pages 601-623 | DOI:10.1007/s00493-020-4419-z

Tai Do Duc

New Constructions of Group-Invariant Butson Hadamard Matrices

Pages 625-644 | DOI:10.1007/s00493-021-4386-z

Tao Feng, Weicong Li

On Transitive Ovoids of Finite Hermitian Polar Spaces

Pages 645-667 | DOI:10.1007/s00493-020-4389-1

Jie Ma, Tianchi Yang

Counting Critical Subgraphs in k-Critical Graphs

Pages 669-694 | DOI:10.1007/s00493-020-4255-1

Alexandr Polyanskii

A Cap Covering Theorem

Pages 695-702 | DOI:10.1007/s00493-021-4554-1

Primož Potočnik, Pablo Spiga

On the Number of Fixed Points of Automorphisms of Vertex-Transitive Graphs

Pages 703-747 | DOI:10.1007/s00493-020-4509-y

Tali Kaufman, Izhar Oppenheim

Erratum to: High Order Random Walks: Beyond Spectral Gap

Pages 749-753 | DOI:10.1007/s00493-021-4451-7

Noga Alon

Explicit Expanders of Every Degree and Size

Pages 447-463 | DOI:10.1007/s00493-020-4429-x

David Conlon, Joonkyung Lee, Oliver Janzer

More on the Extremal Number of Subdivisions

Pages 465-494 | DOI:10.1007/s00493-020-4202-1

Gabriel Currier

New Results on Simplex-Clusters in Set Systems

Pages 495-506 | DOI:10.1007/s00493-020-4441-1

Shaofei Du, Klavdija Kutnar, Dragan Marušič

Resolving The Hamiltonian Problem for Vertex-Transitive Graphs of Order a Product of Two Primes

Pages 507-543 | DOI:10.1007/s00493-020-4384-6

Venkatesan Guruswami, Nicolas Resch, Chaoping Xing

Lossless Dimension Expanders Via Linearized Polynomials and Subspace Designs

Pages 545-579 | DOI:10.1007/s00493-020-4360-1

Tomasz Schoen

A Diophantine Ramsey Theorem

Pages 581-599 | DOI:10.1007/s00493-020-4482-5

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*

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Bolyai Mathematical Society.