Geodesic
Maximum Hypergraphs without Regular Subgraphs
Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 1, pp. 151-166.

Voir la notice de l'article provenant de la source Library of Science

We show that an n-vertex hypergraph with no r-regular subgraphs has at most 2^n−1+r−2 edges. We conjecture that if n gt; r, then every n-vertex hypergraph with no r-regular subgraphs having the maximum number of edges contains a full star, that is, 2^n−1 distinct edges containing a given vertex. We prove this conjecture for n ≥ 425. The condition that n gt; r cannot be weakened.
Keywords: hypergraphs, set system, subgraph, regular graph 
@article{DMGT_2014_34_1_a12,
     author = {Kim, Jaehoon and Kostochka, Alexandr V.},
     title = {Maximum {Hypergraphs} without {Regular} {Subgraphs}},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {151--166},
     publisher = {mathdoc},
     volume = {34},
     number = {1},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2014_34_1_a12/}
}
TY  - JOUR
AU  - Kim, Jaehoon
AU  - Kostochka, Alexandr V.
TI  - Maximum Hypergraphs without Regular Subgraphs
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2014
SP  - 151
EP  - 166
VL  - 34
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2014_34_1_a12/
LA  - en
ID  - DMGT_2014_34_1_a12
ER  - 
%0 Journal Article
%A Kim, Jaehoon
%A Kostochka, Alexandr V.
%T Maximum Hypergraphs without Regular Subgraphs
%J Discussiones Mathematicae. Graph Theory
%D 2014
%P 151-166
%V 34
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2014_34_1_a12/
%G en
%F DMGT_2014_34_1_a12
Kim, Jaehoon; Kostochka, Alexandr V. Maximum Hypergraphs without Regular Subgraphs. Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 1, pp. 151-166. http://geodesic.mathdoc.fr/item/DMGT_2014_34_1_a12/

[1] N. Alon, S. Friedland, and G. Kalai, Regular subgraphs of almost regular graphs, J. Combin. Theory (B) 37 (1984) 79-91. doi:10.1016/0095-8956(84)90047-9

[2] M. Kano, Regular subgraphs of a regular graph, Annals of the New York Academy of Sciences 576 (1989) 281-284. doi:10.1111/j.1749-6632.1989.tb16409.x

[3] D. Mubayi and J. Verstraëte, Two-regular subgraphs of hypergraphs, J. Combin. Theory (B) 99 (2009) 643-655. doi:10.1016/j.jctb.2008.10.005

[4] L. Pyber, Regular subgraphs of dense graphs, Combinatorica 5 (1985) 347-349. doi:10.1007/BF02579250

[5] L. Pyber, V. Rödl, and E. Szemerédi, Dense graphs without 3-regular subgraphs, J. Combin. Theory (B) 63 (1995) 41-54. doi:10.1006/jctb.1995.1004

[6] V. Rödl and B. Wysocka, Note on regular subgraphs, J. Graph Theory 24 (1997) 139-154. doi:10.1002/(SICI)1097-0118(199702)24:2h139::AID-JGT2i3.0.CO;2-R

[7] V.A. Tashkinov, 3-regular subgraphs of 4-regular graphs, Mat. Zametki 36 (1984) 239-259.

[8] V.A. Tashkinov, Regular parts of regular pseudographs, Mat. Zametki 43 (1988) 263-275.