TY - JOUR AU - Bérczi, Kristóf AU - Borbényi, Márton AU - Lovász, László AU - Tóth, László Márton TI - Cycle matroids of graphings: From convergence to duality JF - JOURNAL OF COMBINATORIAL THEORY SERIES B J2 - J COMB THEORY B VL - 178 PY - 2026 SP - 118 EP - 144 PG - 27 SN - 0095-8956 DO - 10.1016/j.jctb.2025.12.003 UR - https://m2.mtmt.hu/api/publication/36692236 ID - 36692236 LA - English DB - MTMT ER - TY - JOUR AU - Bérczi, Kristóf AU - Borbényi, Márton AU - Lovász, László AU - Tóth, László Márton TI - Quotient-Convergence of Submodular Setfunctions JF - COMBINATORICA J2 - COMBINATORICA VL - 46 PY - 2026 IS - 1 PG - 21 SN - 0209-9683 DO - 10.1007/s00493-026-00199-x UR - https://m2.mtmt.hu/api/publication/36926336 ID - 36926336 LA - English DB - MTMT ER - TY - GEN AU - Bérczi, Kristóf AU - Borbényi, Márton AU - László, Lovász AU - Tóth, László Márton TI - Convergent sequences of combinatorial submodular setfunctions PY - 2025 UR - https://m2.mtmt.hu/api/publication/36869969 ID - 36869969 LA - English DB - MTMT ER - TY - GEN AU - Kun, Gábor AU - Tóth, László Márton TI - Graphings with few circulations PY - 2025 UR - https://m2.mtmt.hu/api/publication/36951915 ID - 36951915 LA - English DB - MTMT ER - TY - GEN AU - Héctor, Jardón-Sánchez AU - Tóth, László Márton TI - Skeletons and Spectra: Bernoulli graphings are relatively Ramanujan PY - 2025 UR - https://m2.mtmt.hu/api/publication/36951916 ID - 36951916 LA - English DB - MTMT ER - TY - JOUR AU - Bencs, Ferenc AU - Hruskova, Aranka AU - Tóth, László Márton TI - Factor-of-iid balanced orientation of non-amenable graphs JF - EUROPEAN JOURNAL OF COMBINATORICS J2 - EUR J COMBIN VL - 115 PY - 2024 SN - 0195-6698 DO - 10.1016/j.ejc.2023.103784 UR - https://m2.mtmt.hu/api/publication/34134348 ID - 34134348 N1 - Export Date: 11 September 2023 CODEN: EJOCD Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, NKFIH, KKP-133921, KKP-139502 Funding text 1: The authors would like to thank Miklós Abért, Jan Grebík, Matthieu Joseph, Gábor Kun, Gábor Pete, and Václav Rozhoň for inspiring discussions about various parts of this work. The first author was supported by the NKFIH (National Research, Development and Innovation Office, Hungary) grant KKP-133921 , “Structure, chaos and simplification”. The second and third authors were partially supported by the NKFIH grant KKP-139502 , “Groups and graph limits”. AB - We show that if a non-amenable, quasi-transitive, unimodular graph G has all degrees even then it has a factor-of-iid balanced orientation, meaning each vertex has equal in- and outdegree. This result involves extending earlier spectral-theoretic results on Bernoulli shifts to the Bernoulli graphings of quasi-transitive, unimodular graphs. As a consequence, we also obtain that when G is regular (of either odd or even degree) and bipartite, it has a factor-of-iid perfect matching. This generalizes a result of Lyons and Nazarov beyond transitive graphs. © 2023 The Author(s) LA - English DB - MTMT ER - TY - JOUR AU - Timár, Ádám AU - Tóth, László Márton TI - A full characterization of invariant embeddability of unimodular planar graphs JF - RANDOM STRUCTURES & ALGORITHMS J2 - RANDOM STRUCT ALGOR VL - 64 PY - 2024 IS - 2 SP - 320 EP - 353 PG - 34 SN - 1042-9832 DO - 10.1002/rsa.21188 UR - https://m2.mtmt.hu/api/publication/34199970 ID - 34199970 N1 - Division of Mathematics, The Science Institute, University of Iceland, Reykjavik, Iceland Alfréd Rényi Institute of Mathematics, Budapest, Hungary Chair of Ergodic and Geometric Group Theory, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland Export Date: 27 February 2024 Correspondence Address: Timár, Á.; Division of Mathematics, Iceland; email: madaramit@gmail.com Funding details: European Research Council, ERC, 648017 Funding details: Icelandic Centre for Research, RANNIS, 185233‐051 Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, NKFI, KKP‐139502 Funding text 1: The first author was partially supported by ERC Consolidator Grant 648017 and by Icelandic Research Fund Grant 185233‐051. The second author was partially supported by NKFIH (National Research, Development and Innovation Office, Hungary) grant KKP‐139502, “Groups and graph limits”. AB - When can a unimodular random planar graph be drawn in the Euclidean or the hyperbolic plane in a way that the distribution of the random drawing is isometry‐invariant? This question was answered for one‐ended unimodular graphs in Benjamini and Timar, using the fact that such graphs automatically have locally finite (simply connected) drawings into the plane. For the case of graphs with multiple ends the question was left open. We revisit Halin's graph theoretic characterization of graphs that have a locally finite embedding into the plane. Then we prove that such unimodular random graphs do have a locally finite invariant embedding into the Euclidean or the hyperbolic plane, depending on whether the graph is amenable or not. LA - English DB - MTMT ER - TY - JOUR AU - Bencs, Ferenc AU - Hruskova, Aranka AU - Tóth, László Márton TI - Factor-of-iid Schreier decorations of lattices in Euclidean spaces JF - DISCRETE MATHEMATICS J2 - DISCRETE MATH VL - 347 PY - 2024 IS - 9 PG - 20 SN - 0012-365X DO - 10.1016/j.disc.2024.114056 UR - https://m2.mtmt.hu/api/publication/34760340 ID - 34760340 AB - A Schreier decoration is a combinatorial coding of an action of the free group Fd on the vertex set of a 2d-regular graph. We investigate whether a Schreier decoration exists on various countably infinite transitive graphs as a factor of iid. We show that Zd,d≥3, the square lattice and also the three other Archimedean lattices of even degree have finitary-factor-of-iid Schreier decorations, and exhibit examples of transitive graphs of arbitrary even degree in which obtaining such a decoration as a factor of iid is impossible. We also prove that symmetrical planar lattices with all degrees even have a factor of iid balanced orientation, meaning the indegree of every vertex is equal to its outdegree, and demonstrate that the property of having a factor-of-iid balanced orientation is not invariant under quasi-isometry. LA - English DB - MTMT ER - TY - GEN AU - Kátay, Tamás AU - Tóth, László Márton AU - Vidnyánszky, Zoltán TI - The CSP Dichotomy, the Axiom of Choice, and Cyclic Polymorphisms PY - 2023 UR - https://m2.mtmt.hu/api/publication/34202958 ID - 34202958 AB - We study Constraint Satisfaction Problems (CSPs) in an infinite context. We show that the dichotomy between easy and hard problems -- established already in the finite case -- presents itself as the strength of the corresponding De Bruijin-Erdős-type compactness theorem over ZF. More precisely, if D is a structure, let KD stand for the following statement: for every structure X if every finite substructure of X admits a solution to D, then so does X. We prove that if D admits no cyclic polymorphism, and thus it is NP-complete by the CSP Dichotomy Theorem, then KD is equivalent to the Boolean Prime Ideal Theorem (BPI) over ZF. Conversely, we also show that if D admits a cyclic polymorphism, and thus it is in P, then KD is strictly weaker than BPI. LA - English DB - MTMT ER - TY - JOUR AU - Bencs, Ferenc AU - Tóth, László Márton TI - Invariant random subgroups of groups acting on rooted trees JF - TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY J2 - T AM MATH SOC VL - 374 PY - 2021 SP - 7011 EP - 7040 PG - 30 SN - 0002-9947 DO - 10.1090/tran/8412 UR - https://m2.mtmt.hu/api/publication/31892656 ID - 31892656 N1 - Export Date: 22 August 2022 Funding details: European Research Council, ERC, 648017 Funding details: Mount Allison University, MTA Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, NKFIH, K109684 Funding text 1: Received by the editors February 4, 2020, and, in revised form, November 20, 2020, and December 29, 2020. 2020 Mathematics Subject Classification. Primary 20E08, 20B27, 05C25, 22D40. The first author was partially supported by the MTA Rényi Institute Lendület Limits of Structures Research Group. The second author was supported by the ERC Consolidator Grant 648017. Both authors were partially supported by the Hungarian National Research, Development and Innovation Office, NKFIH grant K109684. AB - We investigate invariant random subgroups in groups acting on rooted trees. Let Alt(f) (T) be the group of finitary even automorphisms of the d-ary rooted tree T. We prove that a nontrivial ergodic invariant random subgroup (IRS) of Alt(f) (T) that acts without fixed points on the boundary of T contains a level stabilizer, in particular it is the random conjugate of a finite index subgroup.Applying the technique to branch groups we prove that an ergodic IRS in a finitary regular branch group contains the derived subgroup of a generalized rigid level stabilizer. We also prove that every weakly branch group has continuum many distinct atomless ergodic IRS's. This extends a result of Benli, Grigorchuk and Nagnibeda who exhibit a group of intermediate growth with this property. LA - English DB - MTMT ER -