@article{MTMT:36692236,
	title = {Cycle matroids of graphings: From convergence to duality},
	url = {https://m2.mtmt.hu/api/publication/36692236},
	author = {Bérczi, Kristóf and Borbényi, Márton and Lovász, László and Tóth, László Márton},
	doi = {10.1016/j.jctb.2025.12.003},
	journal-iso = {J COMB THEORY B},
	journal = {JOURNAL OF COMBINATORIAL THEORY SERIES B},
	volume = {178},
	unique-id = {36692236},
	issn = {0095-8956},
	keywords = {cost; Duality; Graphings; exposed points; Cycle matroid; Matroid limits},
	year = {2026},
	eissn = {1096-0902},
	pages = {118-144},
	orcid-numbers = {Bérczi, Kristóf/0000-0003-0457-4573; Lovász, László/0000-0001-6596-0465; Tóth, László Márton/0000-0002-6821-8060}
}

@article{MTMT:36926336,
	title = {Quotient-Convergence of Submodular Setfunctions},
	url = {https://m2.mtmt.hu/api/publication/36926336},
	author = {Bérczi, Kristóf and Borbényi, Márton and Lovász, László and Tóth, László Márton},
	doi = {10.1007/s00493-026-00199-x},
	journal-iso = {COMBINATORICA},
	journal = {COMBINATORICA},
	volume = {46},
	unique-id = {36926336},
	issn = {0209-9683},
	year = {2026},
	eissn = {1439-6912},
	orcid-numbers = {Bérczi, Kristóf/0000-0003-0457-4573; Lovász, László/0000-0001-6596-0465; Tóth, László Márton/0000-0002-6821-8060}
}

@misc{MTMT:36869969,
	title = {Convergent sequences of combinatorial submodular setfunctions},
	url = {https://m2.mtmt.hu/api/publication/36869969},
	author = {Bérczi, Kristóf and Borbényi, Márton and László, Lovász and Tóth, László Márton},
	unique-id = {36869969},
	year = {2025},
	orcid-numbers = {Bérczi, Kristóf/0000-0003-0457-4573; Tóth, László Márton/0000-0002-6821-8060}
}

@misc{MTMT:36951915,
	title = {Graphings with few circulations},
	url = {https://m2.mtmt.hu/api/publication/36951915},
	author = {Kun, Gábor and Tóth, László Márton},
	unique-id = {36951915},
	year = {2025},
	orcid-numbers = {Tóth, László Márton/0000-0002-6821-8060}
}

@misc{MTMT:36951916,
	title = {Skeletons and Spectra: Bernoulli graphings are relatively Ramanujan},
	url = {https://m2.mtmt.hu/api/publication/36951916},
	author = {Héctor, Jardón-Sánchez and Tóth, László Márton},
	unique-id = {36951916},
	year = {2025},
	orcid-numbers = {Tóth, László Márton/0000-0002-6821-8060}
}

@article{MTMT:34134348,
	title = {Factor-of-iid balanced orientation of non-amenable graphs},
	url = {https://m2.mtmt.hu/api/publication/34134348},
	author = {Bencs, Ferenc and Hruskova, Aranka and Tóth, László Márton},
	doi = {10.1016/j.ejc.2023.103784},
	journal-iso = {EUR J COMBIN},
	journal = {EUROPEAN JOURNAL OF COMBINATORICS},
	volume = {115},
	unique-id = {34134348},
	issn = {0195-6698},
	abstract = {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)},
	year = {2024},
	eissn = {1095-9971},
	orcid-numbers = {Tóth, László Márton/0000-0002-6821-8060}
}

@article{MTMT:34199970,
	title = {A full characterization of invariant embeddability of unimodular planar graphs},
	url = {https://m2.mtmt.hu/api/publication/34199970},
	author = {Timár, Ádám and Tóth, László Márton},
	doi = {10.1002/rsa.21188},
	journal-iso = {RANDOM STRUCT ALGOR},
	journal = {RANDOM STRUCTURES & ALGORITHMS},
	volume = {64},
	unique-id = {34199970},
	issn = {1042-9832},
	abstract = {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.},
	year = {2024},
	eissn = {1098-2418},
	pages = {320-353},
	orcid-numbers = {Tóth, László Márton/0000-0002-6821-8060}
}

@article{MTMT:34760340,
	title = {Factor-of-iid Schreier decorations of lattices in Euclidean spaces},
	url = {https://m2.mtmt.hu/api/publication/34760340},
	author = {Bencs, Ferenc and Hruskova, Aranka and Tóth, László Márton},
	doi = {10.1016/j.disc.2024.114056},
	journal-iso = {DISCRETE MATH},
	journal = {DISCRETE MATHEMATICS},
	volume = {347},
	unique-id = {34760340},
	issn = {0012-365X},
	abstract = {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.},
	year = {2024},
	eissn = {1872-681X},
	orcid-numbers = {Tóth, László Márton/0000-0002-6821-8060}
}

@misc{MTMT:34202958,
	title = {The CSP Dichotomy, the Axiom of Choice, and Cyclic Polymorphisms},
	url = {https://m2.mtmt.hu/api/publication/34202958},
	author = {Kátay, Tamás and Tóth, László Márton and Vidnyánszky, Zoltán},
	unique-id = {34202958},
	abstract = {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.},
	year = {2023},
	orcid-numbers = {Tóth, László Márton/0000-0002-6821-8060; Vidnyánszky, Zoltán/0000-0001-8168-9353}
}

@article{MTMT:31892656,
	title = {Invariant random subgroups of groups acting on rooted trees},
	url = {https://m2.mtmt.hu/api/publication/31892656},
	author = {Bencs, Ferenc and Tóth, László Márton},
	doi = {10.1090/tran/8412},
	journal-iso = {T AM MATH SOC},
	journal = {TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY},
	volume = {374},
	unique-id = {31892656},
	issn = {0002-9947},
	abstract = {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.},
	year = {2021},
	eissn = {1088-6850},
	pages = {7011-7040},
	orcid-numbers = {Tóth, László Márton/0000-0002-6821-8060}
}