More on the Extremal Number of Subdivisions

David Conlon1, Oliver Janzer2, Joonkyung Lee3
1Dept of Mathematics, California Institute of Technology, Pasadena, USA
2Fachbereich Mathematik, Universität Hamburg, Hamburg, Germany
3Department of Mathematics, ETH Zürich, Zürich, Switzerland

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N. Alon, M. Krivelevich and B. Sudakov: Turán numbers of bipartite graphs and related Ramsey-type questions, Combin. Probab. Comput. 12 (2003), 477–494.

N. Alon, L. Rónyai and T. Szabó: Norm-graphs: variations and applications, J. Combin. Theory Ser. B 76 (1999), 280–290.

B. Bukh and D. Conlon: Rational exponents in extremal graph theory, J. Eur. Math. Soc. 20 (2018), 1747–1757.

D. Conlon: Graphs with few paths of prescribed length between any two vertices, Bull. London Math. Soc. 51 (2019), 1015–1021.

D. Conlon and J. Lee: On the extremal number of subdivisions, to appear in Int. Math. Res. Not.

P. Erdos and M. Simonovits: A limit theorem in graph theory, Studia Sci. Math. Hungar. 1 (1966), 51–57.

P. Erdös and A. H. Stone: On the structure of linear graphs, Bull. Amer. Math. Soc. 52 (1946), 1087–1091.

P. Erdős: On the combinatorial problems which I would most like to see solved, Combinatorica 1 (1981), 25–42.

P. Erdős and M. Simonovits: Some extremal problems in graph theory, in: Combinatorial theory and its applications, I, (Proc. Colloq., Balatonfüred, 1969), 377–390. North-Holland, Amsterdam, 1970.

R. J. Faudree and M. Simonovits: On a class of degenerate extremal graph problems, Combinatorica 3 (1983), 83–93.

J. Fox and B. Sudakov: Dependent random choice, Random Structures Algorithms 38 (2011), 68–99.

Z. Füredi: On a Turán type problem of Erdős, Combinatorica 11 (1991), 75–79.

Z. Füredi and M. Simonovits: The history of degenerate (bipartite) extremal graph problems, in: Erdős centennial, volume 25 of Bolyai Soc. Math. Stud., 169–264. János Bolyai Math. Soc., Budapest, 2013.

O. Janzer: Improved bounds for the extremal number of subdivisions, Electron. J. Combin., 26, 2019.

T. Jiang: Compact topological minors in graphs, J. Graph Theory 67 (2011), 139–152.

T. Jiang, J. Ma and L. Yepremyan: On Turán exponents of bipartite graphs, Preprint available at ARXIV1806.02838.

T. Jiang and R. Seiver: Turán numbers of subdivided graphs, SIAM J. Discrete Math. 26 (2012), 1238–1255.

D. Y. Kang, J. Kim and H. Liu: On the rational Turán exponent conjecture, J. Combin. Theory Ser. B 148 (2021), 149–172

Y. Kohayakawa, B. Nagle, V. Rödl and M. Schacht: Weak hypergraph regularity and linear hypergraphs, J. Combin. Theory Ser. B 100 (2010), 151–160.

J. Kollár, L. Rónyai and T. Szabó: Norm-graphs and bipartite Turaán numbers, Combinatorica 16 (1996), 399–406.

A. Kostochka and L. Pyber: Small topological complete subgraphs of “dense” graphs, Combinatorica 8 (1988), 83–86.

T. Kővóri, V. Sós and P. Turán: On a problem of K. Zarankiewicz, Colloq. Math. 3 (1954), 50–57.

J. Verstraëte and J. Williford: Graphs without theta subgraphs, J. Combin. Theory Ser. B 134 (2019), 76–87.