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.

**László Babai**, University of Chicago

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

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

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

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

**Ronald L. Graham**, University of California, San Diego

**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

**Paul D. Seymour**, Princeton University

**József Solymosi**, University of British Columbia

**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.

Asaf Ferber, Vishesh Jain, Benny Sudakov

**Number of 1-factorizations of regular high-degree graphs**

Ervin Gyori, Michael D. Plummer, Dong Ye, Xiaoya Zha

**Cycle Traversability for Claw-free Graphs and Polyhedral Maps**

Alexander Gavrilyuk, Sho Suda, Janos Vidali

**On tight 4-designs in Hamming association schemes**

Andreas F. Holmsen

**Large cliques in hypergraphs with forbidden substructures**

Grigoriy Blekherman, Annie Raymond, Mohit Singh, Rekha Thomas

**Simple Graph Density Inequalities with no Sum of Squares Proofs**

Gergely Harcos, Daniel Soltész

**New bounds on even cycle creating Hamiltonian paths using expander graphs**

Anurag Bishnoi, Ferdinand Ihringer, Valentina Pepe

**A construction for clique-free pseudorandom graphs**

Stefan Glock, Daniela Kuhn, Allan Lo, Deryk Osthus

**On a conjecture of Erdos on locally sparse Steiner triple systems**

Ilkyoo Choi, Daniel W. Cranston, ThĂ©o Pierron

**Degeneracy and Colorings of Squares of Planar Graphs without 4-Cycles**

Karthik C.S., Pasin Manurangsi

**On Closest Pair in Euclidean Metric: Monochromatic is as Hard as Bichromatic**

M. Chapman, N. Linial, Y. Peled

**Expander Graphs -- Both Local and Global**

Paul Seymour, Sophie Spirkl

**Short directed cycles in bipartite digraphs**

Alexander Clifton, Hao Huang

**On almost k-covers of hypercubes**

Ahmad Abdi, Gerard Cornuejols, Dabeen Lee

**Intersecting restrictions in clutters**

Christian Lindorfer, Wolfgang Woess

**The language of self-avoiding walks**

Orit E. Raz, Zvi Shem Tov

**Expanding polynomials: A generalization of the Elekes-Ronyai theorem to d variables**

Stefan Felsner, Tamás Mészáros, Piotr Micek

**Boolean dimension and tree-width**

Chaim Even-Zohar

**Patterns in Random Permutations**

Zdenek Dvorak, Patrice Ossona de Mendez, Hehui Wu

**1-subdivisions, fractional chromatic number and Hall ratio**

Tony Huynh, Gwenael Joret, Piotr Micek, David R. Wood

**Seymour's conjecture on 2-connected graphs of large pathwidth**

Yufei Zhao, Yunkun Zhou

**Impartial Digraphs**

Felix Joos, Stefan Glock, Daniela Kuhn, Deryk Osthus

**Euler tours in hypergraphs**

Zouhaier Ferchiou, Bertrand Guenin

**A short proof of Shih's isomorphism theorem on graphic subspaces**

Misha Rudnev

**On the number of hinges defined by a point set in R^2**

Alexander Sidorenko

**Weakly norming graphs are edge-transitive**

Ashwin Sah

**Improving the 1/3-2/3 Conjecture for Width Two Posets**

Maria Chudnovsky, Alex Scott, Paul Seymour

**Detecting a long odd hole**

Noga Alon, Mrinal Kumar, Ben Lee Volk

Unbalancing Sets and An Almost Quadratic Lower Bound for Syntactically Multilinear Arithmetic Circuits

Pages 149-178 | DOI:10.1007/s00493-019-4009-0

Peter Ayre, Amin Coja-Oghlan, Pu Gao, Noëla Müller

The Satisfiability Threshold For Random Linear Equations

Pages 179-235 | DOI:10.1007/s00493-019-3897-3

John Chiarelli, Pooya Hatami, Michael Saks

An Asymptotically Tight Bound on the Number of Relevant Variables in a Bounded Degree Boolean function

Pages 237-244 | DOI:10.1007/s00493-019-4136-7

Tali Kaufman, Izhar Oppenheim

High Order Random Walks: Beyond Spectral Gap

Pages 245-281 | DOI:10.1007/s00493-019-3847-0

Matthew Kwan, Shoham Letzter, Benny Sudakov, Tuan Tran

Dense Induced Bipartite Subgraphs in Triangle-Free Graphs

Pages 283-305 | DOI:10.1007/s00493-019-4086-0

Robert Connelly, Steven J. Gortler, Louis Theran

Generically Globally Rigid Graphs Have Generic Universally Rigid Frameworks

Pages 1-37 | DOI:10.1007/s00493-018-3694-4

Oliver Ebsen, Mathias Schacht

Homomorphism Thresholds for Odd Cycles

Pages 39-62 | DOI:10.1007/s00493-019-3920-8

He Guo, Lutz Warnke

Packing Nearly Optimal Ramsey R(3,t) Graphs

Pages 63-103 | DOI:10.1007/s00493-019-3921-7

Jie Ma, Bo Ning

Stability Results on the Circumference of a Graph

Pages 105-147 | DOI:10.1007/s00493-019-3843-4

Ron Aharoni, Ron Holzman, Zilin Jiang

Rainbow Fractional Matchings

Pages 1191-1202 | DOI:10.1007/s00493-019-4019-y

Daniela A. Amato

Highly-Arc-Transitive and Descendant-Homogeneous Digraphs with Finite Out-Valency

Pages 1203-1223 | DOI:10.1007/s00493-019-3906-6

Nathan Bowler, Johannes Carmesin, Péter Komjáth, Christian Reiher

The Colouring Number of Infinite Graphs

Pages 1225-1235 | DOI:10.1007/s00493-019-4045-9

Zdeněk Dvořák, Bojan Mohar, Robert Šámal

Exponentially Many Nowhere-Zero ℤ3-, ℤ4-, and ℤ6-Flows

Pages 1237-1253 | DOI:10.1007/s00493-019-3882-x

Peter Frankl, Andrey Kupavskii

Incompatible Intersection Properties

Pages 1255-1266 | DOI:10.1007/s00493-019-4064-6

Radoslav Fulek, Jan Kynčl

Counterexample to an Extension of the Hanani-Tutte Theorem on the Surface of Genus 4

Pages 1267-1279 | DOI:10.1007/s00493-019-3905-7

Yahya O. Hamidoune

Hyper-Atoms Applied to the Critical Pair Theory

Pages 1281-1315 | DOI:10.1007/s00493-019-2429-5

Attila Joó

Vertex-Flames in Countable Rooted Digraphs Preserving an Erdős-Menger Separation for Each Vertex

Pages 1317-1333 | DOI:10.1007/s00493-019-3880-z

Daniel M. Kane, Carlo Sanna, Jeffrey Shallit

Waring’s Theorem for Binary Powers

Pages 1335-1350 | DOI:10.1007/s00493-019-3933-3

Martin Nägele, Benny Sudakov, Rico Zenklusen

Submodular Minimization Under Congruency Constraints

Pages 1351-1386 | DOI:10.1007/s00493-019-3900-1

Sergey Norin, Alex Scott, Paul Seymour, David R. Wood

Clustered Colouring in Minor-Closed Classes

Pages 1387-1412 | DOI:10.1007/s00493-019-3848-z

Neil Robertson, P. D. Seymour, Robin Thomas

Girth Six Cubic Graphs Have Petersen Minors

Pages 1413-1423 | DOI:10.1007/s00493-019-3268-0

Ferdinand Ihringer, Hajime Tanaka

The Independence Number of the Orthogonality Graph in Dimension 2k

Pages 1425-1428 | DOI:10.1007/s00493-019-4134-9

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.

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.