Abstract:
A new statement of a recent theorem of [1, 2] on the maximum number of edges in a hypergraph with forbidden cardinalities of edge intersections is given. This statement is fundamentally simpler than the original one, which makes it possible to obtain important corollaries in combinatorial geometry and Ramsey theory.
This publication is cited in the following 13 articles:
A. V. Berdnikov, A. M. Raigorodskii, “Bounds on Borsuk numbers in distance graphs of a special type”, Problems Inform. Transmission, 57:2 (2021), 136–142
Ph. A. Pushnyakov, A. M. Raigorodskii, “Estimate of the Number of Edges in Special Subgraphs of a Distance Graph”, Math. Notes, 107:2 (2020), 322–332
A. V. Bobu, A. E. Kupriyanov, A. M. Raigorodskii, “A Generalization of Kneser Graphs”, Math. Notes, 107:3 (2020), 392–403
Margarita B. Akhmejanova, Dmitry A. Shabanov, “Equitable colorings of hypergraphs with few edges”, Discrete Applied Mathematics, 276 (2020), 2
A. A. Sagdeev, “On the Chromatic Numbers Corresponding to Exponentially Ramsey Sets”, J Math Sci, 247:3 (2020), 488
L. I. Bogolubsky, A. M. Raigorodskii, “A Remark on Lower Bounds for the Chromatic Numbers of Spaces of Small Dimension with Metrics ℓ1 and ℓ2”, Math. Notes, 105:2 (2019), 180–203
A. A. Sagdeev, “On a Frankl–Wilson Theorem”, Problems Inform. Transmission, 55:4 (2019), 376–395
A. M. Raigorodskii, E. D. Shishunov, “On the Independence Numbers of Some Distance Graphs with Vertices in {–1, 0, 1}n*”, Dokl. Math., 99:2 (2019), 165
A. Sagdeev, “On the Frankl–Rödl theorem”, Izv. Math., 82:6 (2018), 1196–1224
A. A. Sagdeev, “Improved Frankl–Rödl theorem and some of its geometric consequences”, Problems Inform. Transmission, 54:2 (2018), 139–164
A. A. Sagdeev, “Exponentially Ramsey sets”, Problems Inform. Transmission, 54:4 (2018), 372–396
A. A. Sagdeev, “O khromaticheskikh chislakh, sootvetstvuyuschikh eksponentsialno ramseevskim mnozhestvam”, Kombinatorika i teoriya grafov. X, Zap. nauchn. sem. POMI, 475, POMI, SPb., 2018, 174–189
A. M. Raigorodskii, T. V. Trukhan, “On the chromatic numbers of some distance graphs”, Dokl. Math., 98:2 (2018), 515–517