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.

Editors-in-Chief

Imre Bárány, Rényi Institute of Mathematics, Budapest
József Solymosi, University of British Columbia

Founding editors

László Babai, University of Chicago
László Lovász, ELTE Eötvös University, Budapest

Managing editors

Lilla Tóthmérész, ELTE Eötvös University, Budapest
Csaba Király, ELTE Eötvös University, Budapest
Viktor Harangi, Rényi Institute of Mathematics, Budapest

Honorary editors

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

Board of editors

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

Instructions for authors

1. Submission. Manuscripts should be submitted via the editorial system EditFlow. Please use the following link: https://ef.msp.org/submit/combinatorica
2. 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.
3. Notes. Short notes are welcome and processed in an expedited fashion.
4. 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).
5. 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.
6. 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).
7. Reprints. 50 Reprints are provided free of charge upon request. Additional reprints may be ordered.

Volume 44, Issue 4, 2024

Shirshendu Ganguly, Ella Hiesmayr, Kyeongsik Nam
Upper Tail Behavior of the Number of Triangles in Random Graphs with Constant Average Degree
Pages 699-740  |  DOI:10.1007/s00493-024-00086-3

Sahar Diskin, Joshua Erde, Mihyun Kang, Michael Krivelevich
Isoperimetric Inequalities and Supercritical Percolation on High-Dimensional Graphs
Pages 741-784  |  DOI:10.1007/s00493-024-00089-0

Oliver Janzer, Benny Sudakov, István Tomon
Small Subgraphs with Large Average Degree
Pages 785-800  |  DOI:10.1007/s00493-024-00091-6

Gal Yehuda, Amir Yehudayoff
A Lower Bound for Essential Covers of the Cube
Pages 801-815  |  DOI:10.1007/s00493-024-00093-4

Tibor Jordán, Soma Villányi
Globally Linked Pairs of Vertices in Generic Frameworks
Pages 817-838  |  DOI:10.1007/s00493-024-00094-3

Oliver Janzer, Cosmin Pohoata
On the Zarankiewicz Problem for Graphs with Bounded VC-Dimension
Pages 839-848  |  DOI:10.1007/s00493-024-00095-2

Alexandr Kostochka, Ruth Luo, Grace McCourt
A Hypergraph Analog of Dirac’s Theorem for Long Cycles in 2-Connected Graphs
Pages 849-880  |  DOI:10.1007/s00493-024-00096-1

Felix Klingelhoefer, Alantha Newman
Bounding the Chromatic Number of Dense Digraphs by Arc Neighborhoods
Pages 881-895  |  DOI:10.1007/s00493-024-00098-z

Zdeněk Dvořák, Carl Feghali
Solution to a Problem of Grünbaum on the Edge Density of 4-Critical Planar Graphs
Pages 897-907  |  DOI:10.1007/s00493-024-00100-8

Jaehoon Kim, Joonkyung Lee, Hong Liu, Tuan Tran
Rainbow Cycles in Properly Edge-Colored Graphs
Pages 909-919  |  DOI:10.1007/s00493-024-00101-7

Volume 44, Issue 3, 2024

Richard H. Hammack, Paul C. Kainen
Euler’s Theorem for Regular CW-Complexes
Pages 453-465  |  DOI:10.1007/s00493-023-00080-1

Chun-Hung Liu
Defective Coloring is Perfect for Minors
Pages 467-507  |  DOI:10.1007/s00493-024-00081-8

Lior Gishboliner, Zhihan Jin, Benny Sudakov
Ramsey Problems for Monotone Paths in Graphs and Hypergraphs
Pages 509-529  |  DOI:10.1007/s00493-024-00082-7

Colin Defant, Noah Kravitz, Nathan Williams
The Ungar Games
Pages 531-561  |  DOI:10.1007/s00493-024-00083-6

Yotam Dikstein, Irit Dinur, Yuval Filmus, Prahladh Harsha
Boolean Function Analysis on High-Dimensional Expanders
Pages 563-620  |  DOI:10.1007/s00493-024-00084-5

Carolina Benedetti-Velásquez, Kolja Knauer
Lattice Path Matroids and Quotients
Pages 621-650  |  DOI:10.1007/s00493-024-00085-4

Thilo Krill, Max Pitz
The Number of Topological Types of Trees
Pages 651-657  |  DOI:10.1007/s00493-024-00087-2

Eli Berger, Paul Seymour
Bounded-Diameter Tree-Decompositions
Pages 659-674  |  DOI:10.1007/s00493-024-00088-1

António Girão, Freddie Illingworth, Lukas Michel, Michael Savery, Alex Scott
Flashes and Rainbows in Tournaments
Pages 675-690  |  DOI:10.1007/s00493-024-00090-7

Christian Reiher, Tomasz Schoen
Note on the Theorem of Balog, Szemerédi, and Gowers
Pages 691-698  |  DOI:10.1007/s00493-024-00092-5

Volume 44, Issue 2, 2024

Lukas Kölsch, Alexandr Polujan
Value Distributions of Perfect Nonlinear Functions
Pages 231-268  |  DOI:10.1007/s00493-023-00067-y

Benjamin Bedert
On Unique Sums in Abelian Groups
Pages 269-298  |  DOI:10.1007/s00493-023-00069-w

Artūras Dubickas
An Upper Bound for the Height of a Tree with a Given Eigenvalue
Pages 299-310  |  DOI:10.1007/s00493-023-00071-2

Jan Corsten, Walner Mendonça
Tiling Edge-Coloured Graphs with Few Monochromatic Bounded-Degree Graphs
Pages 311-335  |  DOI:10.1007/s00493-023-00072-1

Nguyen Cong Minh, Thanh Vu
A Characterization of Graphs Whose Small Powers of Their Edge Ideals Have a Linear Free Resolution
Pages 337-353  |  DOI:10.1007/s00493-023-00074-z

A. De Schepper, J. Schillewaert, H. Van Maldeghem
On the Generating Rank and Embedding Rank of the Hexagonic Lie Incidence Geometries
Pages 355-392  |  DOI:10.1007/s00493-023-00075-y

Tao Zhang
A Group Ring Approach to Fuglede’s Conjecture in Cyclic Groups
Pages 393-416  |  DOI:10.1007/s00493-023-00076-x

Meike Hatzel, Gwenaël Joret, Piotr Micek, Marcin Pilipczuk, Torsten Ueckerdt, Bartosz Walczak
Tight Bound on Treedepth in Terms of Pathwidth and Longest Path
Pages 417-427  |  DOI:10.1007/s00493-023-00077-w

Yulai Ma, Davide Mattiolo, Eckhard Steffen, Isaak H. Wolf
Edge-Connectivity and Pairwise Disjoint Perfect Matchings in Regular Graphs
Pages 429-440  |  DOI:10.1007/s00493-023-00078-9

Vuong Bui, Hamid Reza Daneshpajouh
A Topological Version of Hedetniemi’s Conjecture for Equivariant Spaces
Pages 441-452  |  DOI:10.1007/s00493-023-00079-8

Top 20 most-cited papers (1981-1999)

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

Top 10 most-cited papers (2000-2009)

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

Top 10 most-cited papers (2010-2019)

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