@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}
}

@inproceedings{MTMT:36244915,
	title = {Matroid Products via Submodular Coupling},
	url = {https://m2.mtmt.hu/api/publication/36244915},
	author = {Bérczi, Kristóf and Gehér, B. and Imolay, A. and Lovász, László and Maga, Balázs and Schwarcz, Tamás Bence},
	booktitle = {STOC '25: Proceedings of the 57th Annual ACM Symposium on Theory of Computing},
	doi = {10.1145/3717823.3718152},
	unique-id = {36244915},
	year = {2025},
	pages = {2074-2085},
	orcid-numbers = {Bérczi, Kristóf/0000-0003-0457-4573; Lovász, László/0000-0001-6596-0465}
}

@article{MTMT:35467361,
	title = {Switchover phenomenon for general graphs},
	url = {https://m2.mtmt.hu/api/publication/35467361},
	author = {Keliger, Dániel and Lovász, László and Móri, Tamás Ferenc and Ódor, Gergely},
	doi = {10.1002/jgt.23184},
	journal-iso = {J GRAPH THEOR},
	journal = {JOURNAL OF GRAPH THEORY},
	volume = {108},
	unique-id = {35467361},
	issn = {0364-9024},
	abstract = {We study SIR-type epidemics (susceptible-infected-resistant) on graphs in two scenarios: (i) when the initial infections start from a well-connected central region and (ii) when initial infections are distributed uniformly. Previously, Ódor et al. demonstrated on a few random graph models that the expectation of the total number of infections undergoes a switchover phenomenon; the central region is more dangerous for small infection rates, while for large rates, the uniform seeding is expected to infect more nodes. We rigorously prove this claim under mild, deterministic assumptions on the underlying graph. If we further assume that the central region has a large enough expansion, the second moment of the degree distribution is bounded and the number of initial infections is comparable to the number of vertices, the difference between the two scenarios is shown to be macroscopic. © 2024 The Author(s). Journal of Graph Theory published by Wiley Periodicals LLC.},
	keywords = {Graph theory; Underlying graphs; General graph; Random graph models; Second moments; Deterministics; infection rates; graph percolation; graph percolation; switchover phenomenon; switchover phenomenon; SIR-type epidemics; SIR-type epidemic; Switchover},
	year = {2025},
	eissn = {1097-0118},
	pages = {560-581},
	orcid-numbers = {Lovász, László/0000-0001-6596-0465; Móri, Tamás Ferenc/0000-0002-9328-7471}
}

@article{MTMT:33678606,
	title = {Random homomorphisms into the orthogonality graph},
	url = {https://m2.mtmt.hu/api/publication/33678606},
	author = {Kunszenti-Kovács, Dávid and Lovász, László and Szegedy, Balázs},
	doi = {10.1016/j.jctb.2024.03.007},
	journal-iso = {J COMB THEORY B},
	journal = {JOURNAL OF COMBINATORIAL THEORY SERIES B},
	volume = {167},
	unique-id = {33678606},
	issn = {0095-8956},
	abstract = {Subgraph densities have been defined, and served as basic tools, both in the case of graphons (limits of dense graph sequences) and graphings (limits of bounded-degree graph sequences). While limit objects have been described for the "middle ranges", the notion of subgraph densities in these limit objects remains elusive. We define subgraph densities in the orthogonality graphs on the unit spheres in dimension d, under appropriate sparsity condition on the subgraphs. These orthogonality graphs exhibit the main difficulties of defining subgraphs the "middle" range, and so we expect their study to serve as a key example to defining subgraph densities in more general Markov spaces.
		The problem can also be formulated as defining and computing random orthogonal representations of graphs. Orthogonal representations have played a role in information theory, optimization, rigidity theory and quantum physics, so to study random ones may be of interest from the point of view of these applications as well.},
	year = {2024},
	eissn = {1096-0902},
	pages = {392-444},
	orcid-numbers = {Kunszenti-Kovács, Dávid/0000-0002-1314-8528; Lovász, László/0000-0001-6596-0465; Szegedy, Balázs/0009-0009-6682-3361}
}

@article{MTMT:34479868,
	title = {Subgraph densities in Markov spaces},
	url = {https://m2.mtmt.hu/api/publication/34479868},
	author = {Kunszenti-Kovács, Dávid and Lovász, László and Szegedy, Balázs},
	doi = {10.1016/j.aim.2023.109414},
	journal-iso = {ADV MATH},
	journal = {ADVANCES IN MATHEMATICS},
	volume = {437},
	unique-id = {34479868},
	issn = {0001-8708},
	abstract = {We generalize subgraph densities, arising in dense graph limit theory, to Markov spaces (symmetric measures on the square of a standard Borel space). More generally, we define an analogue of the set of homomorphisms in the form of a measure on maps of a finite graph into a Markov space. The existence of such homomorphism measures is not always guaranteed, but can be established under rather natural smoothness conditions on the Markov space and sparseness conditions on the graph. This continues a direction in graph limit theory in which such measures are viewed as limits of graph sequences. © 2023 Elsevier Inc.},
	keywords = {Graph limit; Subgraph density; Markov space},
	year = {2024},
	eissn = {1090-2082},
	orcid-numbers = {Kunszenti-Kovács, Dávid/0000-0002-1314-8528; Lovász, László/0000-0001-6596-0465; Szegedy, Balázs/0009-0009-6682-3361}
}

@article{MTMT:35283711,
	title = {The matroid of a graphing ☆},
	url = {https://m2.mtmt.hu/api/publication/35283711},
	author = {Lovász, László},
	doi = {10.1016/j.jctb.2024.08.001},
	journal-iso = {J COMB THEORY B},
	journal = {JOURNAL OF COMBINATORIAL THEORY SERIES B},
	volume = {169},
	unique-id = {35283711},
	issn = {0095-8956},
	keywords = {Matroid; Graph limits; graphing; Submodular setfunction},
	year = {2024},
	eissn = {1096-0902},
	pages = {542-560},
	orcid-numbers = {Lovász, László/0000-0001-6596-0465}
}

@article{MTMT:34686162,
	title = {Impact of physicality on network structure},
	url = {https://m2.mtmt.hu/api/publication/34686162},
	author = {Pósfai, M. and Szegedy, Balázs and Bačić, I. and Blagojević, L. and Abért, Miklós and Kertész, János and Lovász, László and Barabási, A.-L.},
	doi = {10.1038/s41567-023-02267-1},
	journal-iso = {NAT PHYS},
	journal = {NATURE PHYSICS},
	volume = {20},
	unique-id = {34686162},
	issn = {1745-2473},
	abstract = {The emergence of detailed maps of physical networks, such as the brain connectome, vascular networks or composite networks in metamaterials, whose nodes and links are physical entities, has demonstrated the limits of the current network science toolset. Link physicality imposes a non-crossing condition that affects both the evolution and the structure of a network, in a way that the adjacency matrix alone—the starting point of all graph-based approaches—cannot capture. Here, we introduce a meta-graph that helps us to discover an exact mapping between linear physical networks and independent sets, which is a central concept in graph theory. The mapping allows us to analytically derive both the onset of physical effects and the emergence of a jamming transition, and to show that physicality affects the network structure even when the total volume of the links is negligible. Finally, we construct the meta-graphs of several real physical networks, which allows us to predict functional features, such as synapse formation in the brain connectome, that agree with empirical data. Overall, our results show that, to understand the evolution and behaviour of real complex networks, the role of physicality must be fully quantified. © 2023, The Author(s), under exclusive licence to Springer Nature Limited.},
	keywords = {complex networks; Graph theory; Mapping; Toolsets; Network structures; Network science; condition; Nodes and links; VASCULAR NETWORK; connectomes; Meta-graph; 'current; Physical network},
	year = {2024},
	eissn = {1745-2481},
	pages = {142-149},
	orcid-numbers = {Kertész, János/0000-0003-4957-5406; Lovász, László/0000-0001-6596-0465}
}

@article{MTMT:33086820,
	title = {Locally common graphs},
	url = {https://m2.mtmt.hu/api/publication/33086820},
	author = {Csóka, Endre and Hubai, Tamás and Lovász, László},
	doi = {10.1002/jgt.22881},
	journal-iso = {J GRAPH THEOR},
	journal = {JOURNAL OF GRAPH THEORY},
	volume = {102},
	unique-id = {33086820},
	issn = {0364-9024},
	abstract = {Goodman proved that the sum of the number of triangles in a graph on  nodes and its complement is at least ; in other words, this sum is minimized, asymptotically, by a random graph with edge density 1/2. Erdős conjectured that a similar inequality will hold for  in place of , but this was disproved by Thomason. But an analogous statement does hold for some other graphs, which are called <jats:italic>common graphs</jats:italic>. Characterization of common graphs seems, however, out of reach. Franek and Rödl proved that  is common in a weaker, local sense. Using the language of graph limits, we study two versions of locally common graphs. We sharpen a result of Jagger, Štovíček and Thomason by showing that no graph containing  can be locally common, but prove that all such graphs are weakly locally common. We also show that not all connected graphs are weakly locally common.},
	year = {2023},
	eissn = {1097-0118},
	pages = {472-483},
	orcid-numbers = {Lovász, László/0000-0001-6596-0465}
}

@article{MTMT:33106524,
	title = {Cycles of a given length in tournaments},
	url = {https://m2.mtmt.hu/api/publication/33106524},
	author = {Grzesik, A. and Král', D. and Lovász, László and Volec, J.},
	doi = {10.1016/j.jctb.2022.07.007},
	journal-iso = {J COMB THEORY B},
	journal = {JOURNAL OF COMBINATORIAL THEORY SERIES B},
	volume = {158},
	unique-id = {33106524},
	issn = {0095-8956},
	abstract = {We study the asymptotic behavior of the maximum number of directed cycles of a given length in a tournament: let c(l) be the limit of the ratio of the maximum number of cycles of length l in an n-vertex tournament and the expected number of cycles of length l in the random n-vertex tournament, when n tends to infinity. It is well-known that c(3) = 1 and c(4) = 4/3. We show that c(l) = 1 if and only if l is not divisible by four, which settles a conjecture of Bartley and Day. If l is divisible by four, we show that 1 + 2 center dot (2/pi)(l) <= c(l) <= 1 + (2/pi+ o(1))(l) and determine the value c(l) exactly for l = 8. We also give a full description of the asymptotic structure of tournaments with the maximum number of cycles of length l when l is not divisible by four or l is an element of{4, 8}. (c) 2022 Elsevier Inc. All rights reserved.},
	year = {2022},
	eissn = {1096-0902},
	pages = {117-145},
	orcid-numbers = {Lovász, László/0000-0001-6596-0465}
}